diff --git a/citro3d/examples/triangle.rs b/citro3d/examples/triangle.rs
index b367906..f8585e4 100644
--- a/citro3d/examples/triangle.rs
+++ b/citro3d/examples/triangle.rs
@@ -4,7 +4,7 @@
 #![feature(allocator_api)]
 
 use citro3d::macros::include_shader;
-use citro3d::math::{AspectRatio, ClipPlanes, Matrix, Projection, StereoDisplacement};
+use citro3d::math::{AspectRatio, ClipPlanes, Matrix4, Projection, StereoDisplacement};
 use citro3d::render::ClearFlags;
 use citro3d::{attrib, buffer, render, shader};
 use ctru::prelude::*;
@@ -158,9 +158,9 @@ where
 }
 
 struct Projections {
-    left_eye: Matrix,
-    right_eye: Matrix,
-    center: Matrix,
+    left_eye: Matrix4,
+    right_eye: Matrix4,
+    center: Matrix4,
 }
 
 fn calculate_projections() -> Projections {
diff --git a/citro3d/src/math.rs b/citro3d/src/math.rs
index 22634ab..976ddc7 100644
--- a/citro3d/src/math.rs
+++ b/citro3d/src/math.rs
@@ -21,11 +21,40 @@ pub struct IVec(citro3d_sys::C3D_IVec);
 #[doc(alias = "C3D_FQuat")]
 pub struct FQuat(citro3d_sys::C3D_FQuat);
 
+mod mtx {
+    /// An `M`x`N` row-major matrix of `f32`s.
+    #[doc(alias = "C3D_Mtx")]
+    pub struct Matrix<const M: usize, const N: usize>(citro3d_sys::C3D_Mtx);
+
+    impl<const M: usize, const N: usize> Matrix<M, N> {
+        const ROW_SIZE: () = assert!(M == 3 || M == 4);
+        const COLUMN_SIZE: () = assert!(N > 0 && N <= 4);
+
+        // This constructor validates, at compile time, that the
+        // constructed matrix is 3xN or 4xN matrix, where 0 < N ≤ 4.
+        // We put this struct in a submodule to enforce that nothing creates
+        // a Matrix without calling this constructor.
+        #[allow(clippy::let_unit_value)]
+        pub(crate) fn new(value: citro3d_sys::C3D_Mtx) -> Self {
+            let () = Self::ROW_SIZE;
+            let () = Self::COLUMN_SIZE;
+            Self(value)
+        }
+
+        pub(crate) fn as_raw(&self) -> *const citro3d_sys::C3D_Mtx {
+            &self.0
+        }
+    }
+}
+
+pub use mtx::Matrix;
+
+/// A 3x3 row-major matrix of `f32`s.
+pub type Matrix3 = Matrix<3, 3>;
 /// A 4x4 row-major matrix of `f32`s.
-#[doc(alias = "C3D_Mtx")]
-pub struct Matrix(citro3d_sys::C3D_Mtx);
+pub type Matrix4 = Matrix<4, 4>;
 
-impl Matrix {
+impl<const M: usize, const N: usize> Matrix<M, N> {
     /// Construct the zero matrix.
     #[doc(alias = "Mtx_Zeros")]
     pub fn zero() -> Self {
@@ -33,23 +62,21 @@ impl Matrix {
         let mut out = MaybeUninit::uninit();
         unsafe {
             citro3d_sys::Mtx_Zeros(out.as_mut_ptr());
-            Self(out.assume_init())
+            Self::new(out.assume_init())
         }
     }
+}
 
+impl<const N: usize> Matrix<N, N> {
     /// Construct the identity matrix.
     #[doc(alias = "Mtx_Identity")]
     pub fn identity() -> Self {
         let mut out = MaybeUninit::uninit();
         unsafe {
             citro3d_sys::Mtx_Identity(out.as_mut_ptr());
-            Self(out.assume_init())
+            Self::new(out.assume_init())
         }
     }
-
-    pub(crate) fn as_raw(&self) -> *const citro3d_sys::C3D_Mtx {
-        &self.0
-    }
 }
 
 // region: Projection configuration
diff --git a/citro3d/src/math/projection.rs b/citro3d/src/math/projection.rs
index 6833fb9..44bc6e1 100644
--- a/citro3d/src/math/projection.rs
+++ b/citro3d/src/math/projection.rs
@@ -2,14 +2,14 @@ use std::mem::MaybeUninit;
 use std::ops::Range;
 
 use super::{
-    AspectRatio, ClipPlanes, CoordinateOrientation, Matrix, ScreenOrientation, StereoDisplacement,
+    AspectRatio, ClipPlanes, CoordinateOrientation, Matrix4, ScreenOrientation, StereoDisplacement,
 };
 
 /// Configuration for a 3D [projection](https://en.wikipedia.org/wiki/3D_projection).
 /// See specific `Kind` implementations for constructors, e.g.
 /// [`Projection::perspective`] and [`Projection::orthographic`].
 ///
-/// To use the resulting projection, convert it to a [`Matrix`] with [`From`]/[`Into`].
+/// To use the resulting projection, convert it to a [`Matrix`](super::Matrix) with [`From`]/[`Into`].
 #[derive(Clone, Debug)]
 pub struct Projection<Kind> {
     coordinates: CoordinateOrientation,
@@ -122,7 +122,7 @@ impl Projection<Perspective> {
         self,
         left_eye: StereoDisplacement,
         right_eye: StereoDisplacement,
-    ) -> (Matrix, Matrix) {
+    ) -> (Matrix4, Matrix4) {
         // TODO: we might be able to avoid this clone if there was a conversion
         // from &Self to Matrix instead of Self... but it's probably fine for now
         let left = self.clone().stereo(left_eye);
@@ -137,7 +137,7 @@ impl Projection<Perspective> {
     }
 }
 
-impl From<Projection<Perspective>> for Matrix {
+impl From<Projection<Perspective>> for Matrix4 {
     fn from(projection: Projection<Perspective>) -> Self {
         let Perspective {
             vertical_fov_radians,
@@ -182,7 +182,7 @@ impl From<Projection<Perspective>> for Matrix {
             }
         }
 
-        unsafe { Self(result.assume_init()) }
+        unsafe { Self::new(result.assume_init()) }
     }
 }
 
@@ -233,7 +233,7 @@ impl Projection<Orthographic> {
     }
 }
 
-impl From<Projection<Orthographic>> for Matrix {
+impl From<Projection<Orthographic>> for Matrix4 {
     fn from(projection: Projection<Orthographic>) -> Self {
         let make_mtx = match projection.rotation {
             ScreenOrientation::Rotated => citro3d_sys::Mtx_OrthoTilt,
@@ -258,7 +258,7 @@ impl From<Projection<Orthographic>> for Matrix {
                 clip_planes_z.far,
                 projection.coordinates.is_left_handed(),
             );
-            Self(out.assume_init())
+            Self::new(out.assume_init())
         }
     }
 }
diff --git a/citro3d/src/uniform.rs b/citro3d/src/uniform.rs
index c6a1d75..22c7092 100644
--- a/citro3d/src/uniform.rs
+++ b/citro3d/src/uniform.rs
@@ -24,7 +24,8 @@ mod private {
     use crate::math::Matrix;
 
     pub trait Sealed {}
-    impl Sealed for &Matrix {}
+
+    impl<const M: usize, const N: usize> Sealed for &Matrix<M, N> {}
 }
 
 /// A shader uniform. This trait is implemented for types that can be bound to
@@ -36,9 +37,21 @@ pub trait Uniform: private::Sealed {
     fn bind(self, instance: &mut Instance, shader_type: shader::Type, index: Index);
 }
 
-impl Uniform for &Matrix {
-    #[doc(alias = "C3D_FVUnifMtx4x4")]
+impl<const M: usize> Uniform for &Matrix<M, 4> {
+    #[doc(alias = "C34_FVUnifMtxNx4")]
+    #[doc(alias = "C34_FVUnifMtx4x4")]
+    #[doc(alias = "C34_FVUnifMtx3x4")]
+    #[doc(alias = "C34_FVUnifMtx2x4")]
     fn bind(self, _instance: &mut Instance, type_: shader::Type, index: Index) {
-        unsafe { citro3d_sys::C3D_FVUnifMtx4x4(type_.into(), index.into(), self.as_raw()) }
+        unsafe {
+            citro3d_sys::C3D_FVUnifMtxNx4(
+                type_.into(),
+                index.into(),
+                self.as_raw(),
+                // UNWRAP: it should be impossible for end users to construct
+                // a matrix with M > i32::MAX
+                M.try_into().unwrap(),
+            );
+        }
     }
 }