Can every possible linear transformation, at least in 2 or 3 dimensions, be expressed as a simple sequence of scaling, rotation, stretch-squeeze, and reflection?
2026-02-22 20:55:44.1771793744
Intuitive basis for linear transformations (2D/3D matrices)
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Every linear transformation corresponds to a matrix and we know that we can decompose a matrix into its SVD decomposition.
$$A = U\Sigma V^T$$
The orthogonal matrices corresponds to rotation and reflection.
The diagonal matrix corresponds to scaling, stretch-squeeze. However, note that sum singular values can be zero. Hence this corresponds to projection to lower dimensional space.