diff --git a/src/tint/reader/spirv/function.cc b/src/tint/reader/spirv/function.cc
index 9c89c859e9..6c1c9f0f15 100644
--- a/src/tint/reader/spirv/function.cc
+++ b/src/tint/reader/spirv/function.cc
@@ -4136,9 +4136,9 @@ TypedExpression FunctionEmitter::EmitGlslStd450MatrixInverse(
             auto* d = idx(1, 1);
 
             // s * d, -s * b, -s * c, s * a
-            auto* r = pb.mat2x2<f32>(  //
-                pb.Call("vec2f", pb.Mul(s, d), pb.Mul(neg(s), b)),
-                pb.Call("vec2f", pb.Mul(neg(s), c), pb.Mul(s, a)));
+            auto* r = pb.Call("mat2x2f",  //
+                              pb.Call("vec2f", pb.Mul(s, d), pb.Mul(neg(s), b)),
+                              pb.Call("vec2f", pb.Mul(neg(s), c), pb.Mul(s, a)));
             return {mat.type, r};
         }
 
@@ -4156,29 +4156,29 @@ TypedExpression FunctionEmitter::EmitGlslStd450MatrixInverse(
             auto* h = idx(2, 1);
             auto* i = idx(2, 2);
 
-            auto r = pb.Mul(s,               //
-                            pb.mat3x3<f32>(  //
-                                pb.Call("vec3f",
-                                        // e * i - f * h
-                                        sub_mul2(e, i, f, h),
-                                        // c * h - b * i
-                                        sub_mul2(c, h, b, i),
-                                        // b * f - c * e
-                                        sub_mul2(b, f, c, e)),
-                                pb.Call("vec3f",
-                                        // f * g - d * i
-                                        sub_mul2(f, g, d, i),
-                                        // a * i - c * g
-                                        sub_mul2(a, i, c, g),
-                                        // c * d - a * f
-                                        sub_mul2(c, d, a, f)),
-                                pb.Call("vec3f",
-                                        // d * h - e * g
-                                        sub_mul2(d, h, e, g),
-                                        // b * g - a * h
-                                        sub_mul2(b, g, a, h),
-                                        // a * e - b * d
-                                        sub_mul2(a, e, b, d))));
+            auto r = pb.Mul(s,                  //
+                            pb.Call("mat3x3f",  //
+                                    pb.Call("vec3f",
+                                            // e * i - f * h
+                                            sub_mul2(e, i, f, h),
+                                            // c * h - b * i
+                                            sub_mul2(c, h, b, i),
+                                            // b * f - c * e
+                                            sub_mul2(b, f, c, e)),
+                                    pb.Call("vec3f",
+                                            // f * g - d * i
+                                            sub_mul2(f, g, d, i),
+                                            // a * i - c * g
+                                            sub_mul2(a, i, c, g),
+                                            // c * d - a * f
+                                            sub_mul2(c, d, a, f)),
+                                    pb.Call("vec3f",
+                                            // d * h - e * g
+                                            sub_mul2(d, h, e, g),
+                                            // b * g - a * h
+                                            sub_mul2(b, g, a, h),
+                                            // a * e - b * d
+                                            sub_mul2(a, e, b, d))));
             return {mat.type, r};
         }
 
@@ -4234,44 +4234,44 @@ TypedExpression FunctionEmitter::EmitGlslStd450MatrixInverse(
             auto* enfm = sub_mul2(e, n, f, m);
             auto* ejfi = sub_mul2(e, j, f, i);
 
-            auto r = pb.Mul(s,               //
-                            pb.mat4x4<f32>(  //
-                                pb.Call("vec4f",
-                                        // f * kplo - g * jpln + h * jokn
-                                        sub_add_mul3(f, kplo, g, jpln, h, jokn),
-                                        // -b * kplo + c * jpln - d * jokn
-                                        add_sub_mul3(neg(b), kplo, c, jpln, d, jokn),
-                                        // b * gpho - c * fphn + d * fogn
-                                        sub_add_mul3(b, gpho, c, fphn, d, fogn),
-                                        // -b * glhk + c * flhj - d * fkgj
-                                        add_sub_mul3(neg(b), glhk, c, flhj, d, fkgj)),
-                                pb.Call("vec4f",
-                                        // -e * kplo + g * iplm - h * iokm
-                                        add_sub_mul3(neg(e), kplo, g, iplm, h, iokm),
-                                        // a * kplo - c * iplm + d * iokm
-                                        sub_add_mul3(a, kplo, c, iplm, d, iokm),
-                                        // -a * gpho + c * ephm - d * eogm
-                                        add_sub_mul3(neg(a), gpho, c, ephm, d, eogm),
-                                        // a * glhk - c * elhi + d * ekgi
-                                        sub_add_mul3(a, glhk, c, elhi, d, ekgi)),
-                                pb.Call("vec4f",
-                                        // e * jpln - f * iplm + h * injm
-                                        sub_add_mul3(e, jpln, f, iplm, h, injm),
-                                        // -a * jpln + b * iplm - d * injm
-                                        add_sub_mul3(neg(a), jpln, b, iplm, d, injm),
-                                        // a * fphn - b * ephm + d * enfm
-                                        sub_add_mul3(a, fphn, b, ephm, d, enfm),
-                                        // -a * flhj + b * elhi - d * ejfi
-                                        add_sub_mul3(neg(a), flhj, b, elhi, d, ejfi)),
-                                pb.Call("vec4f",
-                                        // -e * jokn + f * iokm - g * injm
-                                        add_sub_mul3(neg(e), jokn, f, iokm, g, injm),
-                                        // a * jokn - b * iokm + c * injm
-                                        sub_add_mul3(a, jokn, b, iokm, c, injm),
-                                        // -a * fogn + b * eogm - c * enfm
-                                        add_sub_mul3(neg(a), fogn, b, eogm, c, enfm),
-                                        // a * fkgj - b * ekgi + c * ejfi
-                                        sub_add_mul3(a, fkgj, b, ekgi, c, ejfi))));
+            auto r = pb.Mul(s,                  //
+                            pb.Call("mat4x4f",  //
+                                    pb.Call("vec4f",
+                                            // f * kplo - g * jpln + h * jokn
+                                            sub_add_mul3(f, kplo, g, jpln, h, jokn),
+                                            // -b * kplo + c * jpln - d * jokn
+                                            add_sub_mul3(neg(b), kplo, c, jpln, d, jokn),
+                                            // b * gpho - c * fphn + d * fogn
+                                            sub_add_mul3(b, gpho, c, fphn, d, fogn),
+                                            // -b * glhk + c * flhj - d * fkgj
+                                            add_sub_mul3(neg(b), glhk, c, flhj, d, fkgj)),
+                                    pb.Call("vec4f",
+                                            // -e * kplo + g * iplm - h * iokm
+                                            add_sub_mul3(neg(e), kplo, g, iplm, h, iokm),
+                                            // a * kplo - c * iplm + d * iokm
+                                            sub_add_mul3(a, kplo, c, iplm, d, iokm),
+                                            // -a * gpho + c * ephm - d * eogm
+                                            add_sub_mul3(neg(a), gpho, c, ephm, d, eogm),
+                                            // a * glhk - c * elhi + d * ekgi
+                                            sub_add_mul3(a, glhk, c, elhi, d, ekgi)),
+                                    pb.Call("vec4f",
+                                            // e * jpln - f * iplm + h * injm
+                                            sub_add_mul3(e, jpln, f, iplm, h, injm),
+                                            // -a * jpln + b * iplm - d * injm
+                                            add_sub_mul3(neg(a), jpln, b, iplm, d, injm),
+                                            // a * fphn - b * ephm + d * enfm
+                                            sub_add_mul3(a, fphn, b, ephm, d, enfm),
+                                            // -a * flhj + b * elhi - d * ejfi
+                                            add_sub_mul3(neg(a), flhj, b, elhi, d, ejfi)),
+                                    pb.Call("vec4f",
+                                            // -e * jokn + f * iokm - g * injm
+                                            add_sub_mul3(neg(e), jokn, f, iokm, g, injm),
+                                            // a * jokn - b * iokm + c * injm
+                                            sub_add_mul3(a, jokn, b, iokm, c, injm),
+                                            // -a * fogn + b * eogm - c * enfm
+                                            add_sub_mul3(neg(a), fogn, b, eogm, c, enfm),
+                                            // a * fkgj - b * ekgi + c * ejfi
+                                            sub_add_mul3(a, fkgj, b, ekgi, c, ejfi))));
             return {mat.type, r};
         }
     }
diff --git a/src/tint/reader/spirv/function_arithmetic_test.cc b/src/tint/reader/spirv/function_arithmetic_test.cc
index aab6168435..538e410781 100644
--- a/src/tint/reader/spirv/function_arithmetic_test.cc
+++ b/src/tint/reader/spirv/function_arithmetic_test.cc
@@ -741,7 +741,7 @@ TEST_F(SpvBinaryArithTestBasic, MatrixTimesScalar) {
     EXPECT_TRUE(fe.EmitBody()) << p->error();
     auto ast_body = fe.ast_body();
     EXPECT_THAT(test::ToString(p->program(), ast_body),
-                HasSubstr("let x_10 : mat2x2<f32> = (x_1 * x_2);"));
+                HasSubstr("let x_10 : mat2x2f = (x_1 * x_2);"));
 }
 
 TEST_F(SpvBinaryArithTestBasic, VectorTimesMatrix) {
@@ -798,7 +798,7 @@ TEST_F(SpvBinaryArithTestBasic, MatrixTimesMatrix) {
     EXPECT_TRUE(fe.EmitBody()) << p->error();
     auto ast_body = fe.ast_body();
     EXPECT_THAT(test::ToString(p->program(), ast_body),
-                HasSubstr("let x_10 : mat2x2<f32> = (x_1 * x_2);"));
+                HasSubstr("let x_10 : mat2x2f = (x_1 * x_2);"));
 }
 
 TEST_F(SpvBinaryArithTestBasic, Dot) {
@@ -838,7 +838,7 @@ TEST_F(SpvBinaryArithTestBasic, OuterProduct) {
     EXPECT_TRUE(fe.EmitBody()) << p->error();
     auto ast_body = fe.ast_body();
     auto got = test::ToString(p->program(), ast_body);
-    EXPECT_THAT(got, HasSubstr("let x_3 : mat2x3<f32> = mat2x3<f32>("
+    EXPECT_THAT(got, HasSubstr("let x_3 : mat2x3f = mat2x3f("
                                "vec3f((x_2.x * x_1.x), (x_2.x * x_1.y), (x_2.x * x_1.z)), "
                                "vec3f((x_2.y * x_1.x), (x_2.y * x_1.y), (x_2.y * x_1.z)));"))
         << got;
@@ -920,7 +920,7 @@ TEST_F(SpvUnaryArithTest, Transpose_2x2) {
     ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions()) << p->error() << "\n" << assembly;
     auto fe = p->function_emitter(100);
     EXPECT_TRUE(fe.EmitBody()) << p->error();
-    const auto* expected = "let x_2 : mat2x2<f32> = transpose(x_1);";
+    const auto* expected = "let x_2 : mat2x2f = transpose(x_1);";
     auto ast_body = fe.ast_body();
     const auto got = test::ToString(p->program(), ast_body);
     EXPECT_THAT(got, HasSubstr(expected)) << got;
@@ -942,7 +942,7 @@ TEST_F(SpvUnaryArithTest, Transpose_2x3) {
     // Note, in the AST dump mat_2_3 means 2 rows and 3 columns.
     // So the column vectors have 2 elements.
     // That is,   %m3v2float is __mat_2_3f32.
-    const auto* expected = "let x_2 : mat3x2<f32> = transpose(x_1);";
+    const auto* expected = "let x_2 : mat3x2f = transpose(x_1);";
     auto ast_body = fe.ast_body();
     const auto got = test::ToString(p->program(), ast_body);
     EXPECT_THAT(got, HasSubstr(expected)) << got;
@@ -961,7 +961,7 @@ TEST_F(SpvUnaryArithTest, Transpose_3x2) {
     ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions()) << p->error() << "\n" << assembly;
     auto fe = p->function_emitter(100);
     EXPECT_TRUE(fe.EmitBody()) << p->error();
-    const auto* expected = "let x_2 : mat2x3<f32> = transpose(x_1);";
+    const auto* expected = "let x_2 : mat2x3f = transpose(x_1);";
     auto ast_body = fe.ast_body();
     const auto got = test::ToString(p->program(), ast_body);
     EXPECT_THAT(got, HasSubstr(expected)) << got;
diff --git a/src/tint/reader/spirv/function_composite_test.cc b/src/tint/reader/spirv/function_composite_test.cc
index bb66d094b7..cb8bc4287b 100644
--- a/src/tint/reader/spirv/function_composite_test.cc
+++ b/src/tint/reader/spirv/function_composite_test.cc
@@ -115,11 +115,10 @@ TEST_F(SpvParserTest_Composite_Construct, Matrix) {
     auto fe = p->function_emitter(100);
     EXPECT_TRUE(fe.EmitBody()) << p->error();
     auto ast_body = fe.ast_body();
-    EXPECT_THAT(test::ToString(p->program(), ast_body),
-                HasSubstr("let x_1 : mat3x2<f32> = mat3x2<f32>("
-                          "vec2f(50.0f, 60.0f), "
-                          "vec2f(60.0f, 50.0f), "
-                          "vec2f(70.0f, 70.0f));"));
+    EXPECT_THAT(test::ToString(p->program(), ast_body), HasSubstr("let x_1 : mat3x2f = mat3x2f("
+                                                                  "vec2f(50.0f, 60.0f), "
+                                                                  "vec2f(60.0f, 50.0f), "
+                                                                  "vec2f(70.0f, 70.0f));"));
 }
 
 TEST_F(SpvParserTest_Composite_Construct, Array) {
@@ -490,9 +489,9 @@ TEST_F(SpvParserTest_CompositeInsert, Matrix) {
     EXPECT_TRUE(fe.EmitBody()) << p->error();
     auto ast_body = fe.ast_body();
     auto body_str = test::ToString(p->program(), ast_body);
-    EXPECT_THAT(body_str, HasSubstr(R"(var x_2_1 : mat3x2<f32> = x_1;
+    EXPECT_THAT(body_str, HasSubstr(R"(var x_2_1 : mat3x2f = x_1;
 x_2_1[2u] = vec2f(50.0f, 60.0f);
-let x_2 : mat3x2<f32> = x_2_1;
+let x_2 : mat3x2f = x_2_1;
 )")) << body_str;
 }
 
@@ -535,9 +534,9 @@ TEST_F(SpvParserTest_CompositeInsert, Matrix_Vector) {
     EXPECT_TRUE(fe.EmitBody()) << p->error();
     auto ast_body = fe.ast_body();
     auto body_str = test::ToString(p->program(), ast_body);
-    EXPECT_THAT(body_str, HasSubstr(R"(var x_2_1 : mat3x2<f32> = x_1;
+    EXPECT_THAT(body_str, HasSubstr(R"(var x_2_1 : mat3x2f = x_1;
 x_2_1[2u] = vec2f(50.0f, 60.0f);
-let x_2 : mat3x2<f32> = x_2_1;
+let x_2 : mat3x2f = x_2_1;
 return;
 )")) << body_str;
 }
diff --git a/src/tint/reader/spirv/function_glsl_std_450_test.cc b/src/tint/reader/spirv/function_glsl_std_450_test.cc
index 9722dc1169..506c8d4aa2 100644
--- a/src/tint/reader/spirv/function_glsl_std_450_test.cc
+++ b/src/tint/reader/spirv/function_glsl_std_450_test.cc
@@ -1420,7 +1420,7 @@ TEST_F(SpvParserTest, GlslStd450_MatrixInverse_mat2x2) {
 
     std::string expected =
         "let s = (1.0f / determinant(m2x2f1));\n"
-        "let x_1 : mat2x2<f32> = mat2x2<f32>(vec2f((s * m2x2f1[1u][1u]), (-(s) * "
+        "let x_1 : mat2x2f = mat2x2f(vec2f((s * m2x2f1[1u][1u]), (-(s) * "
         "m2x2f1[0u][1u])), vec2f((-(s) * m2x2f1[1u][0u]), (s * m2x2f1[0u][0u])));";
 
     EXPECT_THAT(body, HasSubstr(expected)) << body;
@@ -1441,7 +1441,7 @@ TEST_F(SpvParserTest, GlslStd450_MatrixInverse_mat3x3) {
 
     std::string expected =
         "let s = (1.0f / determinant(m3x3f1));\n"
-        "let x_1 : mat3x3<f32> = (s * mat3x3<f32>(vec3f(((m3x3f1[1u][1u] * m3x3f1[2u][2u]) - "
+        "let x_1 : mat3x3f = (s * mat3x3f(vec3f(((m3x3f1[1u][1u] * m3x3f1[2u][2u]) - "
         "(m3x3f1[1u][2u] * m3x3f1[2u][1u])), ((m3x3f1[0u][2u] * m3x3f1[2u][1u]) - (m3x3f1[0u][1u] "
         "* m3x3f1[2u][2u])), ((m3x3f1[0u][1u] * m3x3f1[1u][2u]) - (m3x3f1[0u][2u] * "
         "m3x3f1[1u][1u]))), vec3f(((m3x3f1[1u][2u] * m3x3f1[2u][0u]) - (m3x3f1[1u][0u] * "
@@ -1470,7 +1470,7 @@ TEST_F(SpvParserTest, GlslStd450_MatrixInverse_mat4x4) {
 
     std::string expected =
         "let s = (1.0f / determinant(m4x4f1));\n"
-        "let x_1 : mat4x4<f32> = (s * mat4x4<f32>(vec4f((((m4x4f1[1u][1u] * ((m4x4f1[2u][2u] * "
+        "let x_1 : mat4x4f = (s * mat4x4f(vec4f((((m4x4f1[1u][1u] * ((m4x4f1[2u][2u] * "
         "m4x4f1[3u][3u]) - (m4x4f1[2u][3u] * m4x4f1[3u][2u]))) - (m4x4f1[1u][2u] * "
         "((m4x4f1[2u][1u] * m4x4f1[3u][3u]) - (m4x4f1[2u][3u] * m4x4f1[3u][1u])))) + "
         "(m4x4f1[1u][3u] * ((m4x4f1[2u][1u] * m4x4f1[3u][2u]) - (m4x4f1[2u][2u] * "
@@ -1551,10 +1551,10 @@ TEST_F(SpvParserTest, GlslStd450_MatrixInverse_MultipleInScope) {
 
     std::string expected =
         "let s = (1.0f / determinant(m2x2f1));\n"
-        "let x_1 : mat2x2<f32> = mat2x2<f32>(vec2f((s * m2x2f1[1u][1u]), (-(s) * "
+        "let x_1 : mat2x2f = mat2x2f(vec2f((s * m2x2f1[1u][1u]), (-(s) * "
         "m2x2f1[0u][1u])), vec2f((-(s) * m2x2f1[1u][0u]), (s * m2x2f1[0u][0u])));\n"
         "let s_1 = (1.0f / determinant(m2x2f1));\n"
-        "let x_2 : mat2x2<f32> = mat2x2<f32>(vec2f((s_1 * m2x2f1[1u][1u]), (-(s_1) * "
+        "let x_2 : mat2x2f = mat2x2f(vec2f((s_1 * m2x2f1[1u][1u]), (-(s_1) * "
         "m2x2f1[0u][1u])), vec2f((-(s_1) * m2x2f1[1u][0u]), (s_1 * m2x2f1[0u][0u])));";
 
     EXPECT_THAT(body, HasSubstr(expected)) << body;
diff --git a/src/tint/reader/spirv/function_misc_test.cc b/src/tint/reader/spirv/function_misc_test.cc
index 42874db7f8..2c984d204a 100644
--- a/src/tint/reader/spirv/function_misc_test.cc
+++ b/src/tint/reader/spirv/function_misc_test.cc
@@ -182,7 +182,7 @@ TEST_F(SpvParserTestMiscInstruction, OpUndef_InFunction_Matrix) {
     EXPECT_TRUE(fe.EmitBody()) << p->error();
     auto ast_body = fe.ast_body();
     EXPECT_THAT(test::ToString(p->program(), ast_body),
-                HasSubstr("let x_11 : mat2x2<f32> = mat2x2<f32>();"));
+                HasSubstr("let x_11 : mat2x2f = mat2x2f();"));
 }
 
 TEST_F(SpvParserTestMiscInstruction, OpUndef_InFunction_Array) {
diff --git a/src/tint/reader/spirv/function_var_test.cc b/src/tint/reader/spirv/function_var_test.cc
index 2a56b0c5ab..fd3580be1b 100644
--- a/src/tint/reader/spirv/function_var_test.cc
+++ b/src/tint/reader/spirv/function_var_test.cc
@@ -260,11 +260,10 @@ TEST_F(SpvParserFunctionVarTest, EmitFunctionVariables_MatrixInitializer) {
     EXPECT_TRUE(fe.EmitFunctionVariables());
 
     auto ast_body = fe.ast_body();
-    EXPECT_THAT(test::ToString(p->program(), ast_body),
-                HasSubstr("var x_200 : mat3x2<f32> = mat3x2<f32>("
-                          "vec2f(1.5f, 2.0f), "
-                          "vec2f(2.0f, 3.0f), "
-                          "vec2f(3.0f, 4.0f));"));
+    EXPECT_THAT(test::ToString(p->program(), ast_body), HasSubstr("var x_200 : mat3x2f = mat3x2f("
+                                                                  "vec2f(1.5f, 2.0f), "
+                                                                  "vec2f(2.0f, 3.0f), "
+                                                                  "vec2f(3.0f, 4.0f));"));
 }
 
 TEST_F(SpvParserFunctionVarTest, EmitFunctionVariables_ArrayInitializer) {
diff --git a/src/tint/reader/spirv/parser_impl_module_var_test.cc b/src/tint/reader/spirv/parser_impl_module_var_test.cc
index e77990992b..871edf76d1 100644
--- a/src/tint/reader/spirv/parser_impl_module_var_test.cc
+++ b/src/tint/reader/spirv/parser_impl_module_var_test.cc
@@ -1082,7 +1082,7 @@ TEST_F(SpvModuleScopeVarParserTest, MatrixInitializer) {
     ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions());
     EXPECT_TRUE(p->error().empty());
     const auto module_str = test::ToString(p->program());
-    EXPECT_THAT(module_str, HasSubstr("var<private> x_200 : mat3x2<f32> = mat3x2<f32>("
+    EXPECT_THAT(module_str, HasSubstr("var<private> x_200 : mat3x2f = mat3x2f("
                                       "vec2f(1.5f, 2.0f), "
                                       "vec2f(2.0f, 3.0f), "
                                       "vec2f(3.0f, 4.0f));"));
@@ -1097,7 +1097,7 @@ TEST_F(SpvModuleScopeVarParserTest, MatrixNullInitializer) {
     ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions());
     EXPECT_TRUE(p->error().empty());
     const auto module_str = test::ToString(p->program());
-    EXPECT_THAT(module_str, HasSubstr("var<private> x_200 : mat3x2<f32> = mat3x2<f32>();"));
+    EXPECT_THAT(module_str, HasSubstr("var<private> x_200 : mat3x2f = mat3x2f();"));
 }
 
 TEST_F(SpvModuleScopeVarParserTest, MatrixUndefInitializer) {
@@ -1109,7 +1109,7 @@ TEST_F(SpvModuleScopeVarParserTest, MatrixUndefInitializer) {
     ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions());
     EXPECT_TRUE(p->error().empty());
     const auto module_str = test::ToString(p->program());
-    EXPECT_THAT(module_str, HasSubstr("var<private> x_200 : mat3x2<f32> = mat3x2<f32>();"));
+    EXPECT_THAT(module_str, HasSubstr("var<private> x_200 : mat3x2f = mat3x2f();"));
 
     // This example module emits ok, but is not valid SPIR-V in the first place.
     p->DeliberatelyInvalidSpirv();
@@ -1290,7 +1290,7 @@ TEST_F(SpvModuleScopeVarParserTest, ColMajorDecoration_Dropped) {
     const auto module_str = test::ToString(p->program());
     EXPECT_THAT(module_str, HasSubstr(R"(struct S {
   /* @offset(0) */
-  field0 : mat3x2<f32>,
+  field0 : mat3x2f,
 }
 
 @group(0) @binding(0) var<storage, read_write> myvar : S;
@@ -1321,7 +1321,7 @@ TEST_F(SpvModuleScopeVarParserTest, MatrixStrideDecoration_Natural_Dropped) {
     const auto module_str = test::ToString(p->program());
     EXPECT_THAT(module_str, HasSubstr(R"(struct S {
   /* @offset(0) */
-  field0 : mat3x2<f32>,
+  field0 : mat3x2f,
 }
 
 @group(0) @binding(0) var<storage, read_write> myvar : S;
@@ -1353,7 +1353,7 @@ TEST_F(SpvModuleScopeVarParserTest, MatrixStrideDecoration) {
     EXPECT_THAT(module_str, HasSubstr(R"(struct S {
   /* @offset(0) */
   @stride(64) @internal(disable_validation__ignore_stride)
-  field0 : mat3x2<f32>,
+  field0 : mat3x2f,
 }
 
 @group(0) @binding(0) var<storage, read_write> myvar : S;
@@ -4254,7 +4254,7 @@ TEST_F(SpvModuleScopeVarParserTest, Input_FlattenMatrix) {
     EXPECT_TRUE(p->error().empty());
 
     const auto got = test::ToString(p->program());
-    const std::string expected = R"(var<private> x_1 : mat2x4<f32>;
+    const std::string expected = R"(var<private> x_1 : mat2x4f;
 
 var<private> x_2 : vec4f;
 
@@ -4380,7 +4380,7 @@ TEST_F(SpvModuleScopeVarParserTest, Input_FlattenNested) {
     EXPECT_TRUE(p->error().empty());
 
     const auto got = test::ToString(p->program());
-    const std::string expected = R"(var<private> x_1 : array<mat2x4<f32>, 2u>;
+    const std::string expected = R"(var<private> x_1 : array<mat2x4f, 2u>;
 
 var<private> x_2 : vec4f;
 
@@ -4502,7 +4502,7 @@ TEST_F(SpvModuleScopeVarParserTest, Output_FlattenMatrix) {
     EXPECT_TRUE(p->error().empty());
 
     const auto got = test::ToString(p->program());
-    const std::string expected = R"(var<private> x_1 : mat2x4<f32>;
+    const std::string expected = R"(var<private> x_1 : mat2x4f;
 
 var<private> x_2 : vec4f;
 
diff --git a/src/tint/reader/spirv/parser_type.cc b/src/tint/reader/spirv/parser_type.cc
index b13e2d191a..5abd73922b 100644
--- a/src/tint/reader/spirv/parser_type.cc
+++ b/src/tint/reader/spirv/parser_type.cc
@@ -14,6 +14,7 @@
 
 #include "src/tint/reader/spirv/parser_type.h"
 
+#include <sstream>
 #include <string>
 #include <unordered_map>
 #include <utility>
@@ -216,6 +217,11 @@ Matrix::Matrix(const Type* t, uint32_t c, uint32_t r) : type(t), columns(c), row
 Matrix::Matrix(const Matrix&) = default;
 
 ast::Type Matrix::Build(ProgramBuilder& b) const {
+    if (type->Is<F32>()) {
+        std::ostringstream ss;
+        ss << "mat" << columns << "x" << rows << "f";
+        return b.ty(ss.str());
+    }
     return b.ty.mat(type->Build(b), columns, rows);
 }
 
diff --git a/test/tint/access/let/matrix.spvasm.expected.wgsl b/test/tint/access/let/matrix.spvasm.expected.wgsl
index c8aaa838a7..ddb9c8cd89 100644
--- a/test/tint/access/let/matrix.spvasm.expected.wgsl
+++ b/test/tint/access/let/matrix.spvasm.expected.wgsl
@@ -1,5 +1,5 @@
 fn main_1() {
-  let x_24 : f32 = mat3x3<f32>(vec3f(1.0f, 2.0f, 3.0f), vec3f(4.0f, 5.0f, 6.0f), vec3f(7.0f, 8.0f, 9.0f))[1u].y;
+  let x_24 : f32 = mat3x3f(vec3f(1.0f, 2.0f, 3.0f), vec3f(4.0f, 5.0f, 6.0f), vec3f(7.0f, 8.0f, 9.0f))[1u].y;
   return;
 }
 
diff --git a/test/tint/access/var/matrix.spvasm.expected.wgsl b/test/tint/access/var/matrix.spvasm.expected.wgsl
index 7a655495e4..bc5623421b 100644
--- a/test/tint/access/var/matrix.spvasm.expected.wgsl
+++ b/test/tint/access/var/matrix.spvasm.expected.wgsl
@@ -1,5 +1,5 @@
 fn main_1() {
-  var m : mat3x3<f32> = mat3x3<f32>();
+  var m : mat3x3f = mat3x3f();
   let x_15 : vec3f = m[1i];
   let x_16 : f32 = x_15.y;
   return;
diff --git a/test/tint/bug/oss-fuzz/57795.spv.expected.wgsl b/test/tint/bug/oss-fuzz/57795.spv.expected.wgsl
index 06fd791c2f..026a9ebbf4 100644
--- a/test/tint/bug/oss-fuzz/57795.spv.expected.wgsl
+++ b/test/tint/bug/oss-fuzz/57795.spv.expected.wgsl
@@ -1,5 +1,5 @@
 struct S {
-  field0 : mat3x3<f32>,
+  field0 : mat3x3f,
 }
 
 struct S_1 {
@@ -32,9 +32,9 @@ struct S_7 {
 
 const x_72 = vec4f(0.0f, 0.0f, 0.0f, 0.0f);
 
-const x_73 = mat4x4<f32>(x_72, x_72, x_72, x_72);
+const x_73 = mat4x4f(x_72, x_72, x_72, x_72);
 
-var<private> x_75 : array<mat4x4<f32>, 58u> = array<mat4x4<f32>, 58u>(x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73);
+var<private> x_75 : array<mat4x4f, 58u> = array<mat4x4f, 58u>(x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73, x_73);
 
 const x_77 = vec3f(0.0f, 0.0f, 0.0f);
 
diff --git a/test/tint/bug/tint/1061.spvasm.expected.wgsl b/test/tint/bug/tint/1061.spvasm.expected.wgsl
index b1c8742fd7..016c549861 100644
--- a/test/tint/bug/tint/1061.spvasm.expected.wgsl
+++ b/test/tint/bug/tint/1061.spvasm.expected.wgsl
@@ -10,7 +10,7 @@ var<private> x_GLF_color : vec4f;
 fn main_1() {
   var f : f32;
   var v : vec4f;
-  f = determinant(mat3x3<f32>(vec3f(1.0f, 0.0f, 0.0f), vec3f(0.0f, 1.0f, 0.0f), vec3f(0.0f, 0.0f, 1.0f)));
+  f = determinant(mat3x3f(vec3f(1.0f, 0.0f, 0.0f), vec3f(0.0f, 1.0f, 0.0f), vec3f(0.0f, 0.0f, 1.0f)));
   let x_33 : f32 = f;
   let x_35 : f32 = f;
   let x_37 : f32 = f;
diff --git a/test/tint/bug/tint/1088.spvasm.expected.wgsl b/test/tint/bug/tint/1088.spvasm.expected.wgsl
index 2f6ad19a17..1db30f9668 100644
--- a/test/tint/bug/tint/1088.spvasm.expected.wgsl
+++ b/test/tint/bug/tint/1088.spvasm.expected.wgsl
@@ -1,4 +1,4 @@
-alias Arr = array<mat4x4<f32>, 2u>;
+alias Arr = array<mat4x4f, 2u>;
 
 struct strided_arr {
   @size(16)
@@ -9,7 +9,7 @@ alias Arr_1 = array<strided_arr, 4u>;
 
 struct LeftOver {
   /* @offset(0) */
-  worldViewProjection : mat4x4<f32>,
+  worldViewProjection : mat4x4f,
   /* @offset(64) */
   time : f32,
   /* @offset(80) */
@@ -45,7 +45,7 @@ fn main_1() {
   let x_55 : f32 = p.y;
   let x_57 : f32 = x_14.time;
   p.y = (x_55 + sin((x_57 + 4.0f)));
-  let x_69 : mat4x4<f32> = x_14.worldViewProjection;
+  let x_69 : mat4x4f = x_14.worldViewProjection;
   let x_70 : vec3f = p;
   gl_Position = (x_69 * vec4f(x_70.x, x_70.y, x_70.z, 1.0f));
   let x_83 : vec2f = uv;
diff --git a/test/tint/bug/tint/1520.spvasm.expected.wgsl b/test/tint/bug/tint/1520.spvasm.expected.wgsl
index 25817ce756..bfad42b00f 100644
--- a/test/tint/bug/tint/1520.spvasm.expected.wgsl
+++ b/test/tint/bug/tint/1520.spvasm.expected.wgsl
@@ -8,7 +8,7 @@ struct UniformBuffer {
   /* @offset(48) */
   ucolorGreen_S1_c0 : vec4f,
   /* @offset(64) */
-  umatrix_S1 : mat3x3<f32>,
+  umatrix_S1 : mat3x3f,
 }
 
 @binding(0) @group(0) var<uniform> x_4 : UniformBuffer;
diff --git a/test/tint/bug/tint/1670.spvasm.expected.wgsl b/test/tint/bug/tint/1670.spvasm.expected.wgsl
index 3ab32735d9..ff35a02b7a 100644
--- a/test/tint/bug/tint/1670.spvasm.expected.wgsl
+++ b/test/tint/bug/tint/1670.spvasm.expected.wgsl
@@ -1,19 +1,19 @@
 fn main_1() {
-  var m2i : mat2x2<f32>;
-  var m2 : mat2x2<f32>;
-  var m3i : mat3x3<f32>;
-  var m3 : mat3x3<f32>;
-  var m4i : mat4x4<f32>;
-  var m4 : mat4x4<f32>;
-  let x_12 : mat2x2<f32> = m2;
+  var m2i : mat2x2f;
+  var m2 : mat2x2f;
+  var m3i : mat3x3f;
+  var m3 : mat3x3f;
+  var m4i : mat4x4f;
+  var m4 : mat4x4f;
+  let x_12 : mat2x2f = m2;
   let s = (1.0f / determinant(x_12));
-  m2i = mat2x2<f32>(vec2f((s * x_12[1u][1u]), (-(s) * x_12[0u][1u])), vec2f((-(s) * x_12[1u][0u]), (s * x_12[0u][0u])));
-  let x_19 : mat3x3<f32> = m3;
+  m2i = mat2x2f(vec2f((s * x_12[1u][1u]), (-(s) * x_12[0u][1u])), vec2f((-(s) * x_12[1u][0u]), (s * x_12[0u][0u])));
+  let x_19 : mat3x3f = m3;
   let s_1 = (1.0f / determinant(x_19));
-  m3i = (s_1 * mat3x3<f32>(vec3f(((x_19[1u][1u] * x_19[2u][2u]) - (x_19[1u][2u] * x_19[2u][1u])), ((x_19[0u][2u] * x_19[2u][1u]) - (x_19[0u][1u] * x_19[2u][2u])), ((x_19[0u][1u] * x_19[1u][2u]) - (x_19[0u][2u] * x_19[1u][1u]))), vec3f(((x_19[1u][2u] * x_19[2u][0u]) - (x_19[1u][0u] * x_19[2u][2u])), ((x_19[0u][0u] * x_19[2u][2u]) - (x_19[0u][2u] * x_19[2u][0u])), ((x_19[0u][2u] * x_19[1u][0u]) - (x_19[0u][0u] * x_19[1u][2u]))), vec3f(((x_19[1u][0u] * x_19[2u][1u]) - (x_19[1u][1u] * x_19[2u][0u])), ((x_19[0u][1u] * x_19[2u][0u]) - (x_19[0u][0u] * x_19[2u][1u])), ((x_19[0u][0u] * x_19[1u][1u]) - (x_19[0u][1u] * x_19[1u][0u])))));
-  let x_26 : mat4x4<f32> = m4;
+  m3i = (s_1 * mat3x3f(vec3f(((x_19[1u][1u] * x_19[2u][2u]) - (x_19[1u][2u] * x_19[2u][1u])), ((x_19[0u][2u] * x_19[2u][1u]) - (x_19[0u][1u] * x_19[2u][2u])), ((x_19[0u][1u] * x_19[1u][2u]) - (x_19[0u][2u] * x_19[1u][1u]))), vec3f(((x_19[1u][2u] * x_19[2u][0u]) - (x_19[1u][0u] * x_19[2u][2u])), ((x_19[0u][0u] * x_19[2u][2u]) - (x_19[0u][2u] * x_19[2u][0u])), ((x_19[0u][2u] * x_19[1u][0u]) - (x_19[0u][0u] * x_19[1u][2u]))), vec3f(((x_19[1u][0u] * x_19[2u][1u]) - (x_19[1u][1u] * x_19[2u][0u])), ((x_19[0u][1u] * x_19[2u][0u]) - (x_19[0u][0u] * x_19[2u][1u])), ((x_19[0u][0u] * x_19[1u][1u]) - (x_19[0u][1u] * x_19[1u][0u])))));
+  let x_26 : mat4x4f = m4;
   let s_2 = (1.0f / determinant(x_26));
-  m4i = (s_2 * mat4x4<f32>(vec4f((((x_26[1u][1u] * ((x_26[2u][2u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][2u]))) - (x_26[1u][2u] * ((x_26[2u][1u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][1u])))) + (x_26[1u][3u] * ((x_26[2u][1u] * x_26[3u][2u]) - (x_26[2u][2u] * x_26[3u][1u])))), (((-(x_26[0u][1u]) * ((x_26[2u][2u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][2u]))) + (x_26[0u][2u] * ((x_26[2u][1u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][1u])))) - (x_26[0u][3u] * ((x_26[2u][1u] * x_26[3u][2u]) - (x_26[2u][2u] * x_26[3u][1u])))), (((x_26[0u][1u] * ((x_26[1u][2u] * x_26[3u][3u]) - (x_26[1u][3u] * x_26[3u][2u]))) - (x_26[0u][2u] * ((x_26[1u][1u] * x_26[3u][3u]) - (x_26[1u][3u] * x_26[3u][1u])))) + (x_26[0u][3u] * ((x_26[1u][1u] * x_26[3u][2u]) - (x_26[1u][2u] * x_26[3u][1u])))), (((-(x_26[0u][1u]) * ((x_26[1u][2u] * x_26[2u][3u]) - (x_26[1u][3u] * x_26[2u][2u]))) + (x_26[0u][2u] * ((x_26[1u][1u] * x_26[2u][3u]) - (x_26[1u][3u] * x_26[2u][1u])))) - (x_26[0u][3u] * ((x_26[1u][1u] * x_26[2u][2u]) - (x_26[1u][2u] * x_26[2u][1u]))))), vec4f((((-(x_26[1u][0u]) * ((x_26[2u][2u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][2u]))) + (x_26[1u][2u] * ((x_26[2u][0u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][0u])))) - (x_26[1u][3u] * ((x_26[2u][0u] * x_26[3u][2u]) - (x_26[2u][2u] * x_26[3u][0u])))), (((x_26[0u][0u] * ((x_26[2u][2u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][2u]))) - (x_26[0u][2u] * ((x_26[2u][0u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][0u])))) + (x_26[0u][3u] * ((x_26[2u][0u] * x_26[3u][2u]) - (x_26[2u][2u] * x_26[3u][0u])))), (((-(x_26[0u][0u]) * ((x_26[1u][2u] * x_26[3u][3u]) - (x_26[1u][3u] * x_26[3u][2u]))) + (x_26[0u][2u] * ((x_26[1u][0u] * x_26[3u][3u]) - (x_26[1u][3u] * x_26[3u][0u])))) - (x_26[0u][3u] * ((x_26[1u][0u] * x_26[3u][2u]) - (x_26[1u][2u] * x_26[3u][0u])))), (((x_26[0u][0u] * ((x_26[1u][2u] * x_26[2u][3u]) - (x_26[1u][3u] * x_26[2u][2u]))) - (x_26[0u][2u] * ((x_26[1u][0u] * x_26[2u][3u]) - (x_26[1u][3u] * x_26[2u][0u])))) + (x_26[0u][3u] * ((x_26[1u][0u] * x_26[2u][2u]) - (x_26[1u][2u] * x_26[2u][0u]))))), vec4f((((x_26[1u][0u] * ((x_26[2u][1u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][1u]))) - (x_26[1u][1u] * ((x_26[2u][0u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][0u])))) + (x_26[1u][3u] * ((x_26[2u][0u] * x_26[3u][1u]) - (x_26[2u][1u] * x_26[3u][0u])))), (((-(x_26[0u][0u]) * ((x_26[2u][1u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][1u]))) + (x_26[0u][1u] * ((x_26[2u][0u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][0u])))) - (x_26[0u][3u] * ((x_26[2u][0u] * x_26[3u][1u]) - (x_26[2u][1u] * x_26[3u][0u])))), (((x_26[0u][0u] * ((x_26[1u][1u] * x_26[3u][3u]) - (x_26[1u][3u] * x_26[3u][1u]))) - (x_26[0u][1u] * ((x_26[1u][0u] * x_26[3u][3u]) - (x_26[1u][3u] * x_26[3u][0u])))) + (x_26[0u][3u] * ((x_26[1u][0u] * x_26[3u][1u]) - (x_26[1u][1u] * x_26[3u][0u])))), (((-(x_26[0u][0u]) * ((x_26[1u][1u] * x_26[2u][3u]) - (x_26[1u][3u] * x_26[2u][1u]))) + (x_26[0u][1u] * ((x_26[1u][0u] * x_26[2u][3u]) - (x_26[1u][3u] * x_26[2u][0u])))) - (x_26[0u][3u] * ((x_26[1u][0u] * x_26[2u][1u]) - (x_26[1u][1u] * x_26[2u][0u]))))), vec4f((((-(x_26[1u][0u]) * ((x_26[2u][1u] * x_26[3u][2u]) - (x_26[2u][2u] * x_26[3u][1u]))) + (x_26[1u][1u] * ((x_26[2u][0u] * x_26[3u][2u]) - (x_26[2u][2u] * x_26[3u][0u])))) - (x_26[1u][2u] * ((x_26[2u][0u] * x_26[3u][1u]) - (x_26[2u][1u] * x_26[3u][0u])))), (((x_26[0u][0u] * ((x_26[2u][1u] * x_26[3u][2u]) - (x_26[2u][2u] * x_26[3u][1u]))) - (x_26[0u][1u] * ((x_26[2u][0u] * x_26[3u][2u]) - (x_26[2u][2u] * x_26[3u][0u])))) + (x_26[0u][2u] * ((x_26[2u][0u] * x_26[3u][1u]) - (x_26[2u][1u] * x_26[3u][0u])))), (((-(x_26[0u][0u]) * ((x_26[1u][1u] * x_26[3u][2u]) - (x_26[1u][2u] * x_26[3u][1u]))) + (x_26[0u][1u] * ((x_26[1u][0u] * x_26[3u][2u]) - (x_26[1u][2u] * x_26[3u][0u])))) - (x_26[0u][2u] * ((x_26[1u][0u] * x_26[3u][1u]) - (x_26[1u][1u] * x_26[3u][0u])))), (((x_26[0u][0u] * ((x_26[1u][1u] * x_26[2u][2u]) - (x_26[1u][2u] * x_26[2u][1u]))) - (x_26[0u][1u] * ((x_26[1u][0u] * x_26[2u][2u]) - (x_26[1u][2u] * x_26[2u][0u])))) + (x_26[0u][2u] * ((x_26[1u][0u] * x_26[2u][1u]) - (x_26[1u][1u] * x_26[2u][0u])))))));
+  m4i = (s_2 * mat4x4f(vec4f((((x_26[1u][1u] * ((x_26[2u][2u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][2u]))) - (x_26[1u][2u] * ((x_26[2u][1u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][1u])))) + (x_26[1u][3u] * ((x_26[2u][1u] * x_26[3u][2u]) - (x_26[2u][2u] * x_26[3u][1u])))), (((-(x_26[0u][1u]) * ((x_26[2u][2u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][2u]))) + (x_26[0u][2u] * ((x_26[2u][1u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][1u])))) - (x_26[0u][3u] * ((x_26[2u][1u] * x_26[3u][2u]) - (x_26[2u][2u] * x_26[3u][1u])))), (((x_26[0u][1u] * ((x_26[1u][2u] * x_26[3u][3u]) - (x_26[1u][3u] * x_26[3u][2u]))) - (x_26[0u][2u] * ((x_26[1u][1u] * x_26[3u][3u]) - (x_26[1u][3u] * x_26[3u][1u])))) + (x_26[0u][3u] * ((x_26[1u][1u] * x_26[3u][2u]) - (x_26[1u][2u] * x_26[3u][1u])))), (((-(x_26[0u][1u]) * ((x_26[1u][2u] * x_26[2u][3u]) - (x_26[1u][3u] * x_26[2u][2u]))) + (x_26[0u][2u] * ((x_26[1u][1u] * x_26[2u][3u]) - (x_26[1u][3u] * x_26[2u][1u])))) - (x_26[0u][3u] * ((x_26[1u][1u] * x_26[2u][2u]) - (x_26[1u][2u] * x_26[2u][1u]))))), vec4f((((-(x_26[1u][0u]) * ((x_26[2u][2u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][2u]))) + (x_26[1u][2u] * ((x_26[2u][0u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][0u])))) - (x_26[1u][3u] * ((x_26[2u][0u] * x_26[3u][2u]) - (x_26[2u][2u] * x_26[3u][0u])))), (((x_26[0u][0u] * ((x_26[2u][2u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][2u]))) - (x_26[0u][2u] * ((x_26[2u][0u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][0u])))) + (x_26[0u][3u] * ((x_26[2u][0u] * x_26[3u][2u]) - (x_26[2u][2u] * x_26[3u][0u])))), (((-(x_26[0u][0u]) * ((x_26[1u][2u] * x_26[3u][3u]) - (x_26[1u][3u] * x_26[3u][2u]))) + (x_26[0u][2u] * ((x_26[1u][0u] * x_26[3u][3u]) - (x_26[1u][3u] * x_26[3u][0u])))) - (x_26[0u][3u] * ((x_26[1u][0u] * x_26[3u][2u]) - (x_26[1u][2u] * x_26[3u][0u])))), (((x_26[0u][0u] * ((x_26[1u][2u] * x_26[2u][3u]) - (x_26[1u][3u] * x_26[2u][2u]))) - (x_26[0u][2u] * ((x_26[1u][0u] * x_26[2u][3u]) - (x_26[1u][3u] * x_26[2u][0u])))) + (x_26[0u][3u] * ((x_26[1u][0u] * x_26[2u][2u]) - (x_26[1u][2u] * x_26[2u][0u]))))), vec4f((((x_26[1u][0u] * ((x_26[2u][1u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][1u]))) - (x_26[1u][1u] * ((x_26[2u][0u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][0u])))) + (x_26[1u][3u] * ((x_26[2u][0u] * x_26[3u][1u]) - (x_26[2u][1u] * x_26[3u][0u])))), (((-(x_26[0u][0u]) * ((x_26[2u][1u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][1u]))) + (x_26[0u][1u] * ((x_26[2u][0u] * x_26[3u][3u]) - (x_26[2u][3u] * x_26[3u][0u])))) - (x_26[0u][3u] * ((x_26[2u][0u] * x_26[3u][1u]) - (x_26[2u][1u] * x_26[3u][0u])))), (((x_26[0u][0u] * ((x_26[1u][1u] * x_26[3u][3u]) - (x_26[1u][3u] * x_26[3u][1u]))) - (x_26[0u][1u] * ((x_26[1u][0u] * x_26[3u][3u]) - (x_26[1u][3u] * x_26[3u][0u])))) + (x_26[0u][3u] * ((x_26[1u][0u] * x_26[3u][1u]) - (x_26[1u][1u] * x_26[3u][0u])))), (((-(x_26[0u][0u]) * ((x_26[1u][1u] * x_26[2u][3u]) - (x_26[1u][3u] * x_26[2u][1u]))) + (x_26[0u][1u] * ((x_26[1u][0u] * x_26[2u][3u]) - (x_26[1u][3u] * x_26[2u][0u])))) - (x_26[0u][3u] * ((x_26[1u][0u] * x_26[2u][1u]) - (x_26[1u][1u] * x_26[2u][0u]))))), vec4f((((-(x_26[1u][0u]) * ((x_26[2u][1u] * x_26[3u][2u]) - (x_26[2u][2u] * x_26[3u][1u]))) + (x_26[1u][1u] * ((x_26[2u][0u] * x_26[3u][2u]) - (x_26[2u][2u] * x_26[3u][0u])))) - (x_26[1u][2u] * ((x_26[2u][0u] * x_26[3u][1u]) - (x_26[2u][1u] * x_26[3u][0u])))), (((x_26[0u][0u] * ((x_26[2u][1u] * x_26[3u][2u]) - (x_26[2u][2u] * x_26[3u][1u]))) - (x_26[0u][1u] * ((x_26[2u][0u] * x_26[3u][2u]) - (x_26[2u][2u] * x_26[3u][0u])))) + (x_26[0u][2u] * ((x_26[2u][0u] * x_26[3u][1u]) - (x_26[2u][1u] * x_26[3u][0u])))), (((-(x_26[0u][0u]) * ((x_26[1u][1u] * x_26[3u][2u]) - (x_26[1u][2u] * x_26[3u][1u]))) + (x_26[0u][1u] * ((x_26[1u][0u] * x_26[3u][2u]) - (x_26[1u][2u] * x_26[3u][0u])))) - (x_26[0u][2u] * ((x_26[1u][0u] * x_26[3u][1u]) - (x_26[1u][1u] * x_26[3u][0u])))), (((x_26[0u][0u] * ((x_26[1u][1u] * x_26[2u][2u]) - (x_26[1u][2u] * x_26[2u][1u]))) - (x_26[0u][1u] * ((x_26[1u][0u] * x_26[2u][2u]) - (x_26[1u][2u] * x_26[2u][0u])))) + (x_26[0u][2u] * ((x_26[1u][0u] * x_26[2u][1u]) - (x_26[1u][1u] * x_26[2u][0u])))))));
   return;
 }
 
diff --git a/test/tint/layout/storage/mat2x2/stride/16.spvasm.expected.wgsl b/test/tint/layout/storage/mat2x2/stride/16.spvasm.expected.wgsl
index 2a511a2b85..9d83f4d0c7 100644
--- a/test/tint/layout/storage/mat2x2/stride/16.spvasm.expected.wgsl
+++ b/test/tint/layout/storage/mat2x2/stride/16.spvasm.expected.wgsl
@@ -19,7 +19,7 @@ fn mat2x2_stride_16_to_arr(m : mat2x2<f32>) -> array<strided_arr, 2u> {
 }
 
 fn f_1() {
-  let x_15 : mat2x2<f32> = arr_to_mat2x2_stride_16(ssbo.m);
+  let x_15 : mat2x2f = arr_to_mat2x2_stride_16(ssbo.m);
   ssbo.m = mat2x2_stride_16_to_arr(x_15);
   return;
 }
diff --git a/test/tint/ptr_ref/access/matrix.spvasm.expected.wgsl b/test/tint/ptr_ref/access/matrix.spvasm.expected.wgsl
index 9671518133..57e0ee3e82 100644
--- a/test/tint/ptr_ref/access/matrix.spvasm.expected.wgsl
+++ b/test/tint/ptr_ref/access/matrix.spvasm.expected.wgsl
@@ -1,6 +1,6 @@
 fn main_1() {
-  var m : mat3x3<f32> = mat3x3<f32>();
-  m = mat3x3<f32>(vec3f(1.0f, 2.0f, 3.0f), vec3f(4.0f, 5.0f, 6.0f), vec3f(7.0f, 8.0f, 9.0f));
+  var m : mat3x3f = mat3x3f();
+  m = mat3x3f(vec3f(1.0f, 2.0f, 3.0f), vec3f(4.0f, 5.0f, 6.0f), vec3f(7.0f, 8.0f, 9.0f));
   m[1i] = vec3f(5.0f, 5.0f, 5.0f);
   return;
 }