複選題

15. (5%) Which of the following are correct?
(A) An eigenvalue of a matrix has infinite number of eigenvectors.
(B) If det(A – λI_n) = 0, λ is the eigenvalue of n x n matrix A.
(C) If λ is the eigenvalue of matrix A, the columns of (A -λI_n) are independent.
(D) If λ is the eigenvalue of matrix A, there exist a non-zero vector v such that Av = λv.

(E) The number of the eigenvalue of n x n matrix A may larger than n.

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