Consider a SVD of a $3 \times 2$ matrix $A$, why the product of a $2 \times 2$ $S$ orthogonal matrix $AS$ has orthogonal columns while the product of a $3 \times 3$ orthogonal matrix $SA$ won't?
I don't know how to prove that this is true.
2026-03-29 07:34:41.1774769681
Orthogonal columns of a nonsquare matrix
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