Show that some endomorphsm is not diagonalizable Given an endomorphism $f:V \rightarrow V$ on an $\mathbb{R}$-vector space, prove that if there is $v \in V-\{0\}$ such that $f^2(v)=-v$, then $f$ is not diagonalizable.

Solved. I'm putting the solution. If A is a matrix for f in some basis, then $A^2v=-v$. If $A$ is in diagonal form, $A^2$ has only non-negative entries on the diagonal.
