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1 In general, for a complex matrix A ∈ Cm×n, we get unitary U ∈ Cm×m and V ∈ Cn×n such that U*AV is a real diagonal matrix.
2 Maximal because you have fixed everything: if you ask for any further properties, you may not find any candidate.
3 An RREF reduction, as in Chap. 4, does not accomplish the same result.