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Orthogonal transformation

  • Thread starter ehrenfest
  • Start date
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1. Homework Statement
My statistical mechanics book says that if M is an real, symmetric n by n matrix, and U is the matrix of its eigenvectors as column vectors, then the transformation UMU^{-1} preserves the trace of M. Is that true? If so, is it obvious? If it is true but not obvious, how do you prove it?

2. Homework Equations



3. The Attempt at a Solution
 

Answers and Replies

Dick
Science Advisor
Homework Helper
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It's true and obvious. And U doesn't need to be unitary. Use the cyclic property of trace. Tr(ABC)=Tr(CAB).
 
1,996
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Tr(ABC)=Tr(CAB).
Why is that true?

EDIT: never mind http://en.wikipedia.org/wiki/Trace_(linear_algebra [Broken])
 
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