diff --git a/src/f32/mat4.rs b/src/f32/mat4.rs
index 00c7ef1c..c1432fbe 100644
--- a/src/f32/mat4.rs
+++ b/src/f32/mat4.rs
@@ -389,29 +389,29 @@ impl Mat4 {
     // TODO: make public at some point
     fn look_to_lh(eye: Vec3, dir: Vec3, up: Vec3) -> Self {
         let f = dir.normalize();
+        let s = up.cross(f).normalize();
+        let u = f.cross(s).normalize();
         let (fx, fy, fz) = f.into();
-        let s = f.cross(up);
         let (sx, sy, sz) = s.into();
-        let u = s.cross(f);
         let (ux, uy, uz) = u.into();
-        Self {
-            x_axis: Vec4::new(sx, ux, -fx, 0.0),
-            y_axis: Vec4::new(sy, uy, -fy, 0.0),
-            z_axis: Vec4::new(sz, uz, -fz, 0.0),
-            w_axis: Vec4::new(-s.dot(eye), -u.dot(eye), f.dot(eye), 1.0),
-        }
+        Mat4::new(
+            Vec4::new(sx, ux, fx, 0.0),
+            Vec4::new(sy, uy, fy, 0.0),
+            Vec4::new(sz, uz, fz, 0.0),
+            Vec4::new(-s.dot(eye), -u.dot(eye), -f.dot(eye), 1.0),
+        )
     }
 
     #[inline]
     pub fn look_at_lh(eye: Vec3, center: Vec3, up: Vec3) -> Self {
         glam_assert!(up.is_normalized());
-        Mat4::look_to_lh(eye, center - eye, up)
+        Mat4::look_to_lh(eye, eye - center, up)
     }
 
     #[inline]
     pub fn look_at_rh(eye: Vec3, center: Vec3, up: Vec3) -> Self {
         glam_assert!(up.is_normalized());
-        Mat4::look_to_lh(eye, eye - center, up)
+        Mat4::look_to_lh(eye, center - eye, up)
     }
 
     #[inline]