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

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

P.0.5 Let A ∈ Mn be invertible. Use mathematical induction to prove that (A-1)k = (Ak)-1 for all integers k.

P.0.25 Let A ∈ Mn be idempotent. Show that A is invertible if and only if A = I

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

Solutions

Expert Solution

Colby Messinger answered 1 year ago

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