試題詳解

23. Let A ∈ and x ∈ . Which of the following statements are true?
(A) If A is singular, then O is an eigenvalue of A.
(B) A and share the same eigenvalues and eigenvectors.
(C) If A is diagonalizable, then A has n distinct eigenvalues.
(D) Suppose that A is nonsingular. The condition Ax = λx implies .

(E) Suppose that all the eigenvalues of A are real and positive. Then we have ＞ 0.