April 18th, 2018, 10:10 PM  #1 
Newbie Joined: Apr 2018 From: British Posts: 2 Thanks: 0  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.（Use spectral theorem.) Prove U = g(T) for some polynomial g(t). Thanks. Last edited by skipjack; April 19th, 2018 at 02:09 AM. 
April 18th, 2018, 11:33 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,859 Thanks: 1080 Math Focus: Elementary mathematics and beyond 
You might generate more interest if you posted some work.


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eigenvalues, normal, prove 
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