In a book I read:

"Suppose that{λ1, . . . , λk}is a set ofdistincteigenvalues and{x1, . . . , xk}is the corresponding set of eigenvectors. Thenx1, . . . , xkare linearly independent; that is, eigenvectors associated with distinct eigenvalues are linearly independent."

Assumingλi= 0 for one certain i, that statement does not sound correct to me.

What do you guys think?