試題詳解

16. (5%) Which of the following statements are correct?
(A) If λ is an eigenvalue of an n x n matrix A, then for any
(B) If there exists some such that Av =λv, then λ is an eigenvalue of A.
(C) If two matrices have the same characteristic polynomials, then they have the same eigen- values.
(D) A diagonal matrix is always diagonalizable.
(E) Let A and P be n X n matrices. If the columins of P form a set of n linearly independent eigenvectors of A, then AP is a diagonal matrix.