Thread: eigenvectors/eigenvalues

A ∈ Rn*n and X is an eigenvector of A with eigenvalue ß. P is a nonsingular matrix.

Show directly from the denition that P^1 X is an eigenvector for P^1 AP with eigenvalue ß

im struggling with even starting this? any suggestions would be appreciated

we know that Ax = βx.

so what is P^-1AP(P^-1x)? (hint: P^-1AP(P^-1x) = P^-1(A(P(P^-1x))), and P(P^-1(x)) = x).

thanks for the help ill attempt now