Past exam of the mathematical methods I course of the University of Oxford / 2014 / 12 / iv

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- Solution iv

Solution

Apply the cyclic property of the trace and

B B^{- 1} = I

:

tr (B^{- 1} A B) = tr (A B B^{- 1}) = tr A .

This proves similarity invariance of trace without requiring

A

or

B

to be symmetric.

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