Norm-2 preserving can be done using unitary/orthogonal matrix: $A^*A = I => ||Ax|| = ||x||$
What is the matrix other than identity matrix that can preserve other norms ( norm-1, norm-inf) ?
2026-04-06 11:33:02.1775475182
Norm preserving Matrix properties
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My intuition says that you are limited to +1 or -1 on the diagonal if it should hold for all x and all norms.
General rotations won't survive taxi distance or max in $R^2$ already.