diff --git a/src/intrinsic_table.cc b/src/intrinsic_table.cc
index 8a59ab59d9..276f52cbdc 100644
--- a/src/intrinsic_table.cc
+++ b/src/intrinsic_table.cc
@@ -356,8 +356,9 @@ class OpenSizeMatBuilder : public Builder {
     auto* el = element_builder_->Build(state);
     auto columns = state.open_numbers.at(columns_);
     auto rows = state.open_numbers.at(rows_);
-    return state.ty_mgr.Get<sem::Matrix>(const_cast<sem::Type*>(el), rows,
-                                         columns);
+    auto* column_type =
+        state.ty_mgr.Get<sem::Vector>(const_cast<sem::Type*>(el), rows);
+    return state.ty_mgr.Get<sem::Matrix>(column_type, columns);
   }
 
   std::string str() const override {
diff --git a/src/program_builder.h b/src/program_builder.h
index f9e7a0f82d..9a13b7e1cc 100644
--- a/src/program_builder.h
+++ b/src/program_builder.h
@@ -470,7 +470,7 @@ class ProgramBuilder {
       type = MaybeCreateTypename(type);
       return {type.ast ? builder->create<ast::Matrix>(type, rows, columns)
                        : nullptr,
-              type.sem ? builder->create<sem::Matrix>(type, rows, columns)
+              type.sem ? builder->create<sem::Matrix>(vec(type, rows), columns)
                        : nullptr};
     }
 
@@ -486,7 +486,7 @@ class ProgramBuilder {
       return {type.ast
                   ? builder->create<ast::Matrix>(source, type, rows, columns)
                   : nullptr,
-              type.sem ? builder->create<sem::Matrix>(type, rows, columns)
+              type.sem ? builder->create<sem::Matrix>(vec(type, rows), columns)
                        : nullptr};
     }
 
diff --git a/src/resolver/resolver.cc b/src/resolver/resolver.cc
index cea5eb34bb..488bc6c870 100644
--- a/src/resolver/resolver.cc
+++ b/src/resolver/resolver.cc
@@ -347,8 +347,9 @@ const sem::Type* Resolver::Type(const ast::Type* ty) {
     }
     if (auto* t = ty->As<ast::Matrix>()) {
       if (auto* el = Type(t->type())) {
-        return builder_->create<sem::Matrix>(const_cast<sem::Type*>(el),
-                                             t->rows(), t->columns());
+        auto* column_type = builder_->create<sem::Vector>(
+            const_cast<sem::Type*>(el), t->rows());
+        return builder_->create<sem::Matrix>(column_type, t->columns());
       }
       return nullptr;
     }
@@ -1958,8 +1959,10 @@ bool Resolver::Binary(ast::BinaryExpression* expr) {
     auto* rhs_vec = rhs_type->As<sem::Vector>();
     const sem::Type* result_type = nullptr;
     if (lhs_mat && rhs_mat) {
-      result_type = builder_->create<sem::Matrix>(
-          lhs_mat->type(), lhs_mat->rows(), rhs_mat->columns());
+      auto* column_type =
+          builder_->create<sem::Vector>(lhs_mat->type(), lhs_mat->rows());
+      result_type =
+          builder_->create<sem::Matrix>(column_type, rhs_mat->columns());
     } else if (lhs_mat && rhs_vec) {
       result_type =
           builder_->create<sem::Vector>(lhs_mat->type(), lhs_mat->rows());
@@ -2886,9 +2889,9 @@ const sem::Type* Resolver::Canonical(const sem::Type* type) {
           const_cast<sem::Type*>(make_canonical(v->type())), v->size());
     }
     if (auto* m = ct->As<Matrix>()) {
-      return builder_->create<Matrix>(
-          const_cast<sem::Type*>(make_canonical(m->type())), m->rows(),
-          m->columns());
+      auto* column_type =
+          builder_->create<sem::Vector>(make_canonical(m->type()), m->rows());
+      return builder_->create<Matrix>(column_type, m->columns());
     }
     if (auto* ac = ct->As<AccessControl>()) {
       return builder_->create<AccessControl>(ac->access_control(),
diff --git a/src/resolver/resolver_test_helper.h b/src/resolver/resolver_test_helper.h
index 910a23004d..cd9f5a64a3 100644
--- a/src/resolver/resolver_test_helper.h
+++ b/src/resolver/resolver_test_helper.h
@@ -239,17 +239,20 @@ sem::Type* sem_vec4(const ProgramBuilder::TypesBuilder& ty) {
 
 template <create_sem_type_func_ptr create_type>
 sem::Type* sem_mat2x2(const ProgramBuilder::TypesBuilder& ty) {
-  return ty.builder->create<sem::Matrix>(create_type(ty), 2, 2);
+  auto* column_type = ty.builder->create<sem::Vector>(create_type(ty), 2u);
+  return ty.builder->create<sem::Matrix>(column_type, 2u);
 }
 
 template <create_sem_type_func_ptr create_type>
 sem::Type* sem_mat3x3(const ProgramBuilder::TypesBuilder& ty) {
-  return ty.builder->create<sem::Matrix>(create_type(ty), 3, 3);
+  auto* column_type = ty.builder->create<sem::Vector>(create_type(ty), 3u);
+  return ty.builder->create<sem::Matrix>(column_type, 3u);
 }
 
 template <create_sem_type_func_ptr create_type>
 sem::Type* sem_mat4x4(const ProgramBuilder::TypesBuilder& ty) {
-  return ty.builder->create<sem::Matrix>(create_type(ty), 4, 4);
+  auto* column_type = ty.builder->create<sem::Vector>(create_type(ty), 4u);
+  return ty.builder->create<sem::Matrix>(column_type, 4u);
 }
 
 template <create_sem_type_func_ptr create_type>
diff --git a/src/sem/matrix_type.cc b/src/sem/matrix_type.cc
index 07c173f807..b8b965c556 100644
--- a/src/sem/matrix_type.cc
+++ b/src/sem/matrix_type.cc
@@ -15,18 +15,22 @@
 #include "src/sem/matrix_type.h"
 
 #include "src/program_builder.h"
+#include "src/sem/vector_type.h"
 
 TINT_INSTANTIATE_TYPEINFO(tint::sem::Matrix);
 
 namespace tint {
 namespace sem {
 
-Matrix::Matrix(Type* subtype, uint32_t rows, uint32_t columns)
-    : subtype_(subtype), rows_(rows), columns_(columns) {
-  TINT_ASSERT(rows > 1);
-  TINT_ASSERT(rows < 5);
-  TINT_ASSERT(columns > 1);
-  TINT_ASSERT(columns < 5);
+Matrix::Matrix(Vector* column_type, uint32_t columns)
+    : subtype_(column_type->type()),
+      column_type_(column_type),
+      rows_(column_type->size()),
+      columns_(columns) {
+  TINT_ASSERT(rows_ > 1);
+  TINT_ASSERT(rows_ < 5);
+  TINT_ASSERT(columns_ > 1);
+  TINT_ASSERT(columns_ < 5);
 }
 
 Matrix::Matrix(Matrix&&) = default;
@@ -47,8 +51,8 @@ std::string Matrix::FriendlyName(const SymbolTable& symbols) const {
 
 Matrix* Matrix::Clone(CloneContext* ctx) const {
   // Clone arguments outside of create() call to have deterministic ordering
-  auto* ty = ctx->Clone(type());
-  return ctx->dst->create<Matrix>(ty, rows_, columns_);
+  auto* column_type = ctx->Clone(ColumnType());
+  return ctx->dst->create<Matrix>(column_type, columns_);
 }
 
 }  // namespace sem
diff --git a/src/sem/matrix_type.h b/src/sem/matrix_type.h
index 2dd6ed2576..4a4be0ff1a 100644
--- a/src/sem/matrix_type.h
+++ b/src/sem/matrix_type.h
@@ -22,14 +22,16 @@
 namespace tint {
 namespace sem {
 
+// Forward declaration
+class Vector;
+
 /// A matrix type
 class Matrix : public Castable<Matrix, Type> {
  public:
   /// Constructor
-  /// @param subtype type matrix type
-  /// @param rows the number of rows in the matrix
+  /// @param column_type the type of a column of the matrix
   /// @param columns the number of columns in the matrix
-  Matrix(Type* subtype, uint32_t rows, uint32_t columns);
+  Matrix(Vector* column_type, uint32_t columns);
   /// Move constructor
   Matrix(Matrix&&);
   ~Matrix() override;
@@ -41,6 +43,9 @@ class Matrix : public Castable<Matrix, Type> {
   /// @returns the number of columns in the matrix
   uint32_t columns() const { return columns_; }
 
+  /// @returns the column-vector type of the matrix
+  Vector* ColumnType() const { return column_type_; }
+
   /// @returns the name for this type
   std::string type_name() const override;
 
@@ -56,6 +61,7 @@ class Matrix : public Castable<Matrix, Type> {
 
  private:
   Type* const subtype_;
+  Vector* const column_type_;
   uint32_t const rows_;
   uint32_t const columns_;
 };
diff --git a/src/sem/matrix_type_test.cc b/src/sem/matrix_type_test.cc
index f94faa3cd1..9b3df83b2e 100644
--- a/src/sem/matrix_type_test.cc
+++ b/src/sem/matrix_type_test.cc
@@ -24,7 +24,8 @@ using MatrixTest = TestHelper;
 
 TEST_F(MatrixTest, Creation) {
   I32 i32;
-  Matrix m{&i32, 2, 4};
+  Vector c{&i32, 2};
+  Matrix m{&c, 4};
   EXPECT_EQ(m.type(), &i32);
   EXPECT_EQ(m.rows(), 2u);
   EXPECT_EQ(m.columns(), 4u);
@@ -32,7 +33,8 @@ TEST_F(MatrixTest, Creation) {
 
 TEST_F(MatrixTest, Is) {
   I32 i32;
-  Matrix m{&i32, 2, 3};
+  Vector c{&i32, 2};
+  Matrix m{&c, 4};
   Type* ty = &m;
   EXPECT_FALSE(ty->Is<AccessControl>());
   EXPECT_FALSE(ty->Is<Alias>());
@@ -51,12 +53,15 @@ TEST_F(MatrixTest, Is) {
 
 TEST_F(MatrixTest, TypeName) {
   I32 i32;
-  Matrix m{&i32, 2, 3};
+  Vector c{&i32, 2};
+  Matrix m{&c, 3};
   EXPECT_EQ(m.type_name(), "__mat_2_3__i32");
 }
 
 TEST_F(MatrixTest, FriendlyName) {
-  Matrix m{ty.i32(), 3, 2};
+  I32 i32;
+  Vector c{&i32, 3};
+  Matrix m{&c, 2};
   EXPECT_EQ(m.FriendlyName(Symbols()), "mat2x3<i32>");
 }
 
diff --git a/src/transform/transform_test.cc b/src/transform/transform_test.cc
index f287f57dd7..b83defc334 100644
--- a/src/transform/transform_test.cc
+++ b/src/transform/transform_test.cc
@@ -58,7 +58,8 @@ TEST_F(CreateASTTypeForTest, Basic) {
 
 TEST_F(CreateASTTypeForTest, Matrix) {
   auto* mat = create([](ProgramBuilder& b) {
-    return b.create<sem::Matrix>(b.create<sem::F32>(), 2, 3);
+    auto* column_type = b.create<sem::Vector>(b.create<sem::F32>(), 2u);
+    return b.create<sem::Matrix>(column_type, 3u);
   });
   ASSERT_TRUE(mat->Is<ast::Matrix>());
   ASSERT_TRUE(mat->As<ast::Matrix>()->type()->Is<ast::F32>());