 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2014/12/iv/solution

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

B

to be symmetric.

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