- Thread starter
- #1

- Feb 5, 2012

- 1,621

I just want to know what "positive" means in this context? Is it positive definiteness or something? I mean, we cannot speak about the positivity or the negativity of the function \(f\) since it gives out complex values.

**Problem:**

Prove that the function \(f:\, M_{n}(\mathbb{C})\times M_{n}(\mathbb{C})\rightarrow \mathbb{C}\) given by \(f(X,\,Y)=\mbox{Tr }(X^{t}\overline{Y})\) is non-singular. Is \(f\) positive?