Relation between Positive definite matrix and strictly convex function

UPDATE: As pointed out in the comments by @Erik, positive definiteness is a sufficient condition for strict convexity. However in these case, positive definiteness is indeed directly implied since the second derivative is a positive definitive matrix.

PREVIOUS ANSWER: For any twice differentiable function, it is strictly convex if and only if, the Hessian matrix is positive definite. You can find it from any standard textbook on convex optimization. Now here the function at hand is $z^TMz$ which is clearly twice differentiable (by virtue of being quadratic). Now the Hessian of this function is $M$ (please verify yourself, it helped me a lot to memorize it). So $M$ should be positive definite for that quadratic function to be convex.