It's not quite true, is it...? Av = cv v is an eigenvector, c the corresponding eigenvalue (A^-1)Av = (A^-1)cv v = c(A^-1)v (1/c)v = (A^-1)v So

It's not quite true, is it...? Av = cv v is an eigenvector, c the corresponding eigenvalue (A^-1)Av = (A^-1)cv v = c(A^-1)v (1/c)v = (A^-1)v So if c is an eigenvalue of A, then 1/c is an eigenvalue of (A^-1). (c can't be 0 because A is invertible, I think.)