Linear algebra trace question?
Let T be a linear operator on V . Define the trace of T as the trace of the
matrix representation of T, with respect to a basis of V . Use the fact that
tr(AB) = tr(BA) for square matrices A and B to prove that the definition
of trace does not depend on the basis thus chosen.
I calculated that the tr(A) = tr(BAB^-1) but where do i go from there?
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That's it.
If two matrices represent the same linear operator but with different bases, then they are similar. By showing
tr(A) = tr(BAB^-1)
for arbitrary square matrices A,B where B is invertible, you've shown that any two similar matrices have the same trace, which is precisely what you were asked to show.