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April 18th, 2018, 10:10 PM   #1
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Unhappy Prove U is normal

I am stuck on this question. Please help.

Suppose that V is a finite dimensional inner product space over C and dim V = n; let T be a normal linear transformation of V.

If U is a linear transformation of V and T has n distinct eigenvalues such that TU=UT, prove U is normal.´╝łUse spectral theorem.) Prove U = g(T) for some polynomial g(t).

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Last edited by skipjack; April 19th, 2018 at 02:09 AM.
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April 18th, 2018, 11:33 PM   #2
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