"Let $A,M \in ,M_n(K)$ where $A$ is a symmetrical matrix $K$ is a field. If $A =^tMM$ then A is semi-definite positive."
I have seen similar questions asked but each considers either the real vector spaces or the invertible matrices.
I know if that if $A, M \in M_n(\Bbb R)$ then $^t(Mx)(Mx)\ge 0$ for every $v \in V$ but if we consdier complex numbers that statament might not hold true. Also M is not necessarly an invertible element so $A$ and $I_n$ are not necessarly congruent in this case.
Is this statament true, and if yes, how do you prove it in the complex case?