Let $A$ be an $n \times n$ symmetric positive definite matrix, and let $M$ be an $n \times m$ matrix.
Show that the matrix $M^tAM$ is symmetric positive definite (spd).
I am trying to use the definition of an spd matrix, showing that the inner product is $\geq 0$. So, $\langle x^tM^tAM,x\rangle \geq 0$ and since $A$ is spd, it is also diagonazable $A=V^tLV$. Am I going in the right direction?