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: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond 
You might generate more interest if you posted some work.


Tags 
eigenvalues, normal, prove 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Prove H is a normal subgroup of G  msv  Abstract Algebra  1  March 25th, 2015 03:34 AM 
normal to the curve/normal to the circle  cheyb93  Calculus  7  October 29th, 2012 01:11 PM 
Product normal implies components normal  cos5000  Real Analysis  3  November 18th, 2009 08:52 PM 
prove prove prove. currently dont know where to post  qweiop90  Algebra  1  July 31st, 2008 06:27 AM 
prove prove prove. currently dont know where to post  qweiop90  New Users  1  December 31st, 1969 04:00 PM 