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  3. p.0.2 show that (a) the diagonal entries of a herm

P.0.2 Show that (a) the diagonal entries of a Hermitian matrix are real; (b) the diagonal...

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Advance Math

P.0.2 Show that (a) the diagonal entries of a Hermitianmatrix are real; (b) the diagonal entries of a skew-Hermitianmatrix purely imaginary; c) the diagonal entries of askew-symmetric matrix are zero.

P.0.5 Let A ? Mn be invertible. Use mathematicalinduction to prove that (A-1)k = (Ak)-1 for all integersk.

P.0.25 Let A ? Mn be idempotent. Show that A isinvertible if and only if A = I


P.0.26 Let A,B ? Mn be idempotent. Show that tr((A-B)3) =tr(A-B).

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