# Math Help - Eigenvalues

1. ## Eigenvalues

Just a quick question, given a matrix A and a diagonal matrix D

Does DA(D^-1) always have the same eigenvalues as A?

Thanks.

2. Originally Posted by Talamari
Just a quick question, given a matrix A and a diagonal matrix D

Does DA(D^-1) always have the same eigenvalues as A?

Thanks.

Well, yes...but D doesn't even need to be diagonal: this is true for any invertible matrix D, since then $A\,,\,DAD^{-1}$ are similar and thus they have the same characteristic polynomial.

Tonio