diff --git a/math/float_types.hpp b/math/float_types.hpp
index b1b852c..e88b9bb 100644
--- a/math/float_types.hpp
+++ b/math/float_types.hpp
@@ -1,11 +1,11 @@
 #pragma once
 
-#include "math/vec2.hpp"
-#include "math/vec3.hpp"
-#include "math/vec4.hpp"
-#include "math/mat2x2.hpp"
-#include "math/mat3x3.hpp"
-#include "math/mat4x4.hpp"
+#include "vec2.hpp"
+#include "vec3.hpp"
+#include "vec4.hpp"
+#include "mat2x2.hpp"
+#include "mat3x3.hpp"
+#include "mat4x4.hpp"
 
 using vec2 = vec<2, float>;
 using vec3 = vec<3, float>;
diff --git a/math/mat.hpp b/math/mat.hpp
new file mode 100644
index 0000000..3fbeaea
--- /dev/null
+++ b/math/mat.hpp
@@ -0,0 +1,26 @@
+#pragma once
+
+template <int R, int C, typename T>
+struct mat;
+
+template <int R, int C, typename T>
+inline constexpr typename mat<R, C, T>::col_type
+col(mat<R, C, T> const& m, int c)
+{
+  typename mat<R, C, T>::col_type v;
+  for (int r = 0; r < R; r++) {
+    v[r] = m[r][c];
+  }
+  return v;
+}
+
+template <int R, typename T>
+inline constexpr vec<3, T>
+col(mat<R, 4, T> const& m, int c)
+{
+  vec<3, T> v;
+  for (int r = 0; r < 3; r++) {
+    v[r] = m[r][c];
+  }
+  return v;
+}
diff --git a/math/mat2x2.hpp b/math/mat2x2.hpp
index da5f33c..8b8aec7 100644
--- a/math/mat2x2.hpp
+++ b/math/mat2x2.hpp
@@ -2,12 +2,10 @@
 
 #include <utility>
 #include "vec2.hpp"
-
-template <int R, int C, typename T>
-struct mat;
+#include "mat.hpp"
 
 //
-// mat4x4
+// mat2x2
 //
 
 template <typename T>
diff --git a/math/mat3x3.hpp b/math/mat3x3.hpp
index 1117179..3bd64d9 100644
--- a/math/mat3x3.hpp
+++ b/math/mat3x3.hpp
@@ -2,9 +2,7 @@
 
 #include <utility>
 #include "vec3.hpp"
-
-template <int R, int C, typename T>
-struct mat;
+#include "mat.hpp"
 
 //
 // mat3x3
diff --git a/math/mat4x4.hpp b/math/mat4x4.hpp
index 3008ef9..bcddf1f 100644
--- a/math/mat4x4.hpp
+++ b/math/mat4x4.hpp
@@ -2,9 +2,7 @@
 
 #include <utility>
 #include "vec4.hpp"
-
-template <int R, int C, typename T>
-struct mat;
+#include "mat.hpp"
 
 //
 // mat4x4
diff --git a/math/transform.hpp b/math/transform.hpp
index 8e60b21..0e18fc4 100644
--- a/math/transform.hpp
+++ b/math/transform.hpp
@@ -1,5 +1,9 @@
 #pragma once
 
+#include "math.hpp"
+#include "vec.hpp"
+#include "mat.hpp"
+
 template<typename T>
 inline constexpr mat<4, 4, T> translate(vec<3, T> t)
 {