Let A and B be Hermitian matrices with AB = BA and let N = A +(adsbygoogle = window.adsbygoogle || []).push({}); iB.

1) Show that N is normal.

2) Show that A = 1/2(N+N*) (* = conjugate transpose) and find a formula for B.

3) Let U be a unitary matrix such that U*NU is a diagonal matrix. Show that U*AU and U*BU is diagonal matrices.

I had no problems with 1) and 2) but I simply can't figure out 3)... Please help.

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# Complex matrix problem

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