Linear algebra problem

  • Thread starter zheng89120
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Homework Statement



let:
Trace(A) = Ʃ(i=1..n) (ei|A|ei)

Show that trace is independent of the orthonormal basis chosen.

Homework Equations



linear algebra

The Attempt at a Solution



trace is related to the eigenvalues, which are constant?
 

Answers and Replies

  • #2
Dick
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Homework Statement



let:
Trace(A) = Ʃ(i=1..n) (ei|A|ei)

Show that trace is independent of the orthonormal basis chosen.

Homework Equations



linear algebra

The Attempt at a Solution



trace is related to the eigenvalues, which are constant?

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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