I am confused about the concept semidefinite matrix:
Why all the eigenvalues of $A = B^t . B$ are non-negative? My thought is that: $$X . (A . X) = X . ((B^t . B) . X) = X . (B^t . (B . X)) = (B . X) . (B . X) = (|B.X|)^2 $$ Because $(|B.X|)^2$ cannot be negative, $X . (A . X) \ge 0$ no matter what $X$ is. But I am not sure how the fact of $X . (A . X) >= 0$ is related to $A.X=eigenvalue[A].X$ and is therefore related to that all eigenvalues of A are non-negative.
Thank you for any clarification.