Let the eigenvalues of the matrix A be 11, A2, . . An and the linearly ww w wwwww www independent eigenvectors corresponding to these eigenvalues V1,V2,..., Vn . (S [V¡V2 . . Vn]nxn) by placing the vectors V1,V2,..., Vn in each column of A is the eigenvalue of V1,V2,..., Vn placed on the wwww the S matrix; If the matrix wmwm w m ww. diagonal, prove that, diagonal matrix. Also show that eAt = A = SAS-1 (A diag[A1 ^2 . ..An]nxn) with in the w ww uwww SeAt s-1 ww w w w w w e

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