Why usually consider unitary matrices to deﬁne image transforms?
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Because, on a inner product space (i.e. Euclidean space, or Hilbert space in more generality) unitaries are precisely the linear isometric bijections. You want a bijection if you want not to lose information, and you want isometric if you want the distances in your image to be preserved. The linearity, together with the isometry, imply that orthogonality is preserved.