I came across this problem but do not know how to approach it. Could someone point me in the right direction?
Let $T:\mathbb{R}^4\to\mathbb{R}^4$ be a linear transformation. Then which of the following is true?
(A) $T$ must have some real eigenvalues which may be less than 4 in number.
(B) $T$ may not have any real eigenvalues at all.
(C) $T$ must have infinitely many real eigenvalues.
(D) $T$ must have exactly 4 real eigenvalues.