• Use the CS decomposition to solve each of the following problems, even though other approaches are possible. A given A ∈ Mn, m is a contraction if its largest singular value is less than or equal to 1. Let ∈ M2 be unitary. (a) Show that |u11| = |u22| and |u21| = |u12| = (1 − |u11|2)1/2. (b) Show that U is diagonally unitarily similar to a complex symmetric matrix.
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