diff --git a/math/mat3x3.hpp b/math/mat3x3.hpp
new file mode 100644
index 0000000..5442125
--- /dev/null
+++ b/math/mat3x3.hpp
@@ -0,0 +1,115 @@
+#pragma once
+
+#include <utility>
+#include "vec3.hpp"
+
+template <int R, int C, typename T>
+struct mat;
+
+//
+// mat3x3
+//
+
+template <typename T>
+struct mat<3, 3, T>
+{
+  typedef vec<3, T> row_type;
+  typedef vec<3, T> col_type;
+
+private:
+  row_type value[3];
+
+public:
+  inline constexpr mat();
+
+  inline constexpr mat
+  (
+    T const& a00, T const& a01, T const& a02,
+    T const& a10, T const& a11, T const& a12,
+    T const& a20, T const& a21, T const& a22
+  );
+
+  inline static constexpr int length() { return 3; }
+
+  inline constexpr typename mat<3, 3, T>::row_type const &
+  operator[](int i) const;
+
+  void operator=(const mat<3, 3, T>&) = delete;
+
+};
+
+
+template<typename T>
+inline constexpr mat<3, 3, T>::mat()
+  : value{std::move(row_type(1, 0, 0)),
+	  std::move(row_type(0, 1, 0)),
+          std::move(row_type(0, 0, 1))}
+{ }
+
+template<typename T>
+inline constexpr mat<3, 3, T>::mat
+(
+  T const& a00, T const& a01, T const& a02,
+  T const& a10, T const& a11, T const& a12,
+  T const& a20, T const& a21, T const& a22
+)
+  : value{std::move(row_type(a00, a01, a02)),
+	  std::move(row_type(a10, a11, a12)),
+          std::move(row_type(a20, a21, a22))}
+{ }
+
+template <typename T>
+inline constexpr typename mat<3, 3, T>::row_type const &
+mat<3, 3, T>::operator[](int i) const
+{
+  switch (i)
+  {
+  default: [[fallthrough]];
+  case 0:
+    return value[0];
+  case 1:
+    return value[1];
+  case 2:
+    return value[2];
+  }
+}
+
+template<typename T>
+inline constexpr mat<3, 3, T> operator*(mat<3, 3, T> const& m1, mat<3, 3, T> const& m2)
+{
+#define c(i, j) (                               \
+    m1[i][0] * m2[0][j]                         \
+  + m1[i][1] * m2[1][j]                         \
+  + m1[i][2] * m2[2][j] )
+
+  return mat<3, 3, T>(c(0,0), c(0,1), c(0,2),
+                      c(1,0), c(1,1), c(1,2),
+                      c(2,0), c(2,1), c(2,2));
+#undef c
+}
+
+template<typename T>
+inline constexpr typename mat<3, 3, T>::row_type operator*
+(
+  mat<3, 3, T> const& m,
+  typename mat<3, 3, T>::col_type const& v
+)
+{
+#define c(i) (                                  \
+    m[i][0] * v[0]                              \
+  + m[i][1] * v[1]                              \
+  + m[i][2] * v[2] )
+
+  return typename mat<3, 3, T>::row_type(c(0), c(1), c(2));
+#undef c
+}
+
+template<typename T>
+inline constexpr mat<3, 3, T> transpose(mat<3, 3, T> const& m)
+{
+  return mat<3, 3, T>(
+    m[0][0], m[1][0], m[2][0],
+    m[0][1], m[1][1], m[2][1],
+    m[0][2], m[1][2], m[2][2]
+  );
+}
diff --git a/math/mat4x3.hpp b/math/mat4x3.hpp
new file mode 100644
index 0000000..6de9c6f
--- /dev/null
+++ b/math/mat4x3.hpp
@@ -0,0 +1,119 @@
+#pragma once
+
+#include <utility>
+#include "vec4.hpp"
+
+template <int R, int C, typename T>
+struct mat;
+
+//
+// mat4x4
+//
+
+template <typename T>
+struct mat<4, 3, T>
+{
+  typedef vec<4, T> row_type;
+  typedef vec<4, T> col_type;
+
+private:
+  row_type value[4];
+
+public:
+  inline constexpr mat();
+
+  inline constexpr mat
+  (
+    T const& a00, T const& a01, T const& a02, T const& a03,
+    T const& a10, T const& a11, T const& a12, T const& a13,
+    T const& a20, T const& a21, T const& a22, T const& a23,
+  );
+
+  inline static constexpr int length() { return 4; }
+
+  inline constexpr typename mat<4, 3, T>::row_type const &
+  operator[](int i) const;
+
+  void operator=(const mat<4, 3, T>&) = delete;
+
+};
+
+
+template<typename T>
+inline constexpr mat<4, 3, T>::mat()
+  : value{std::move(row_type(1, 0, 0, 0)),
+	  std::move(row_type(0, 1, 0, 0)),
+          std::move(row_type(0, 0, 1, 0)),
+{ }
+
+template<typename T>
+inline constexpr mat<4, 3, T>::mat
+(
+  T const& a00, T const& a01, T const& a02, T const& a03,
+  T const& a10, T const& a11, T const& a12, T const& a13,
+  T const& a20, T const& a21, T const& a22, T const& a23,
+)
+  : value{std::move(row_type(a00, a01, a02, a03)),
+	  std::move(row_type(a10, a11, a12, a13)),
+          std::move(row_type(a20, a21, a22, a23)),
+{ }
+
+template <typename T>
+inline constexpr typename mat<4, 3, T>::row_type const &
+mat<4, 3, T>::operator[](int i) const
+{
+  switch (i)
+  {
+  default: [[fallthrough]];
+  case 0:
+    return value[0];
+  case 1:
+    return value[1];
+  case 2:
+    return value[2];
+  }
+}
+
+template<typename T>
+inline constexpr mat<4, 3, T> operator*(mat<4, 3, T> const& m1, mat<4, 3, T> const& m2)
+{
+  constexpr T row3[4] = {0, 0, 0, 1};
+#define c(i, j) (                               \
+    m1[i][0] * m2[0][j]                         \
+  + m1[i][1] * m2[1][j]                         \
+  + m1[i][2] * m2[2][j]                         \
+  + m1[i][3] *  row3[j] )
+
+  return mat<4, 3, T>(c(0,0), c(0,1), c(0,2), c(0,3),
+                      c(1,0), c(1,1), c(1,2), c(1,3),
+                      c(2,0), c(2,1), c(2,2), c(2,3),
+                      c(3,0), c(3,1), c(3,2), c(3,3));
+#undef c
+}
+
+template<typename T>
+inline constexpr typename mat<4, 3, T>::row_type operator*
+(
+  mat<4, 3, T> const& m,
+  typename mat<4, 3, T>::col_type const& v
+)
+{
+#define c(i) (                                  \
+    m[i][0] * v[0]                              \
+  + m[i][1] * v[1]                              \
+  + m[i][2] * v[2]                              \
+  + m[i][3] * v[3] )
+
+  return typename mat<4, 3, T>::row_type(c(0), c(1), c(2));
+#undef c
+}
+
+template<typename T>
+inline constexpr mat<4, 3, T> transpose(mat<4, 3, T> const& m)
+{
+  return mat<4, 3, T>(
+    m[0][0], m[1][0], m[2][0], m[3][0],
+    m[0][1], m[1][1], m[2][1], m[3][1],
+    m[0][2], m[1][2], m[2][2], m[3][2],
+  );
+}