The same rotation produces different rotation matrices. For example this: let R1 = Transform(rotation: simd_quatf(from: [1, 0, 0], to: [0, 1, 0])) let R2 = Transform(rotation: simd_quatf(from: [2, 0, 0], to: [0, 2, 0])) print(R1.matrix) print(R2.matrix) outputs simd_float4x4([[-1.1920929e-07, 1.0000001, 0.0, 0.0], [-1.0000001, -1.1920929e-07, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 1.0]]) simd_float4x4([[-3.0000005, 4.0000005, 0.0, 0.0], [-4.0000005, -3.0000005, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 1.0]]) With some cleaning up the matrices look like this // R1 [0, -1, 0, 0] [1, 0, 0, 0] [0, 0, 1, 0] [0, 0, 0, 1] // R2 [-3, -4, 0, 0] [ 4, -3, 0, 0] [ 0, 0, 1, 0] [ 0, 0, 0, 1] We see that R2 actually scales its input. A pure rotation should have a scale of 1. Another disagreement occurs when evaluating the Transform's scale. For example this print(R2.scale) print(Transform(matrix: R2).scale) outputs this SIMD3<Float>(1.0, 1.0, 1.0) SIMD3<Float>(5.000001, 5.000001, 1.0) Why are the scales different for the same exact transform? Also, the rotation angles do not agree. This print(R2.rotation.angle * 180 / .pi) print(Transform(matrix: R2.matrix).rotation.angle * 180 / .pi) produces 90.00001 126.8699 90 degrees is the correct rotation angle. Where does 126.87 degrees come from?