25. (4 points) Which of the following statements are correct?

(A) If Q is orthogonal, then det(Q) = = +1.

(B) Let A be a real n x n matrix. Then A is symmetric if and only if A is orthogonally
equivalent to a real diagonal matrix.

(C) Let A E Rixm be a matrix whose characteristic polynomial splits over R. Then A
is orthogonally equivalent to a real upper triangular matrix.

(D) Let T be a self-adjoint (Hermitian) operator on a finite-dimensional inner product
space V. Then every eigenvalue of T is positive.

(E) Let T be a self-adjoint (Hermitian) operator on a finite-dimensional inner product
space V. Then every eigenvalue of T is negative.