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Homework Help: Linear algebra problem

  1. Nov 2, 2011 #1
    1. The problem statement, all variables and given/known data

    Trace(A) = Ʃ(i=1..n) (ei|A|ei)

    Show that trace is independent of the orthonormal basis chosen.

    2. Relevant equations

    linear algebra

    3. The attempt at a solution

    trace is related to the eigenvalues, which are constant?
  2. jcsd
  3. Nov 2, 2011 #2


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    Science Advisor
    Homework Helper

    IF A a diagonalizable and IF the ei happen to be eigenvectors, then sure, it's easy to see the trace is the sum of the eigenvalues. But how does that help you show it's basis independent? How do you write the relation between A and A written in a different basis?
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