diff --git a/src/vec/vec.h b/src/vec/vec.h
index 3c278a0..c94116c 100644
--- a/src/vec/vec.h
+++ b/src/vec/vec.h
@@ -17,15 +17,18 @@ struct u64x2 {
   u64 y;
 };
 
-typedef struct f32x2 V2f;
-struct f32x2 {
-  union {
-    f32 x;
-    f32 u;
-  };
-  union {
-    f32 y;
-    f32 v;
+typedef union f32x2 V2f;
+union f32x2 {
+  f32 elements[2];
+  struct {
+    union {
+      f32 x;
+      f32 u;
+    };
+    union {
+      f32 y;
+      f32 v;
+    };
   };
 };
 
@@ -66,6 +69,25 @@ struct u64x3 {
   u64 z;
 };
 
+typedef union f32_3x2 M3x2f;
+union f32_3x2 {
+  V2f rows[3];
+  struct {
+    V2f row0;
+    V2f row1;
+    V2f row2;
+  };
+};
+
+typedef union f32_2x3 M2x3f;
+union f32_2x3 {
+  V3f rows[2];
+  struct {
+    V3f row0;
+    V3f row1;
+  };
+};
+
 typedef union f32_3x3 M3x3f;
 union f32_3x3 {
   V3f rows[3];
@@ -146,6 +168,32 @@ MAKE_LIST_TYPE(V2f);
       .z = V1.x * V2.y - V1.y * V2.x,                                          \
   })
 
+#define mat3x2_transpose(MAT)                                                  \
+  ((M2x3f){                                                                    \
+      .row0 = {.x = MAT.row0.x, .y = MAT.row1.x, .z = MAT.row2.x},             \
+      .row1 = {.x = MAT.row0.y, .y = MAT.row1.y, .z = MAT.row2.y},             \
+  })
+
+#define mat2x3_mul_vec3(MAT, V)                                                \
+  ((V2f){                                                                      \
+      .elements[0] = dot_v3(MAT.rows[0], V),                                   \
+      .elements[1] = dot_v3(MAT.rows[1], V),                                   \
+  })
+
+#define mat3x3_transpose(MAT)                                                  \
+  ((M3x3f){                                                                    \
+      .row0 = {.x = MAT.row0.x, .y = MAT.row1.x, .z = MAT.row2.x},             \
+      .row1 = {.x = MAT.row0.y, .y = MAT.row1.y, .z = MAT.row2.y},             \
+      .row2 = {.x = MAT.row0.z, .y = MAT.row1.z, .z = MAT.row2.z},             \
+  })
+
+#define mat3x3_mul_vec3(MAT, V)                                                \
+  ((V3f){                                                                      \
+      .elements[0] = dot_v3(MAT.rows[0], V),                                   \
+      .elements[1] = dot_v3(MAT.rows[1], V),                                   \
+      .elements[2] = dot_v3(MAT.rows[2], V),                                   \
+  })
+
 #define mat4x4_identity                                                        \
   ((M4x4f){                                                                    \
       .row0 = {1.0f, 0.0f, 0.0f, 0.0f},                                        \