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We say the a matrix A is similar to a matrix B if there is some...

We say the a matrix A is similar to a matrix B if there is some invertible matrix P so that B=P^-1 AP.

Show that if A and B are similar matrices and b is an eigenvalue for B, then b is also an eigenvalue for A. How would an eigenvector for B associated with b compare to an eigenvector for A?

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