Let l1, l2 . . . , ln be the eigenvalues of a matrix A. What are the eigenvalues of A^2?
there must be some relation bwn. the eigenvalues of A and A^2 matrix which i cannot see it.. Please assist.
Many thanks.
Suppose is an eigenvalue associated to some vector ; then , and , so is an eigenvalue of .
Note that the converse does not always hold; could have no eigenvalues while could. For instance if rotates the plane by an angle of , then has no (real) eigenvalues but does.