This question has been answered before, but I want to check if my solution using minimal polynomials is good.

A projection matrix satisfies $M^2 = M$, so it satisfies the polynomial equation $M(M-1) = 0$. Thus the minimal polynomial must be either $M$, $M-1$, or $M(M-1)$. Since in all cases the polynomial factors into distinct linear factors, the matrix is diagonaliazable.

  • 3
    $\begingroup$ Perfectly fine. Just saying $X(X-1)$ is a polynomial with simple roots is enough, though. $\endgroup$ – Gabriel Romon Mar 12 '16 at 22:40

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.