Here is a small question:
I was reading a problem in a textbook where the question is: Prove that $A$ is invertible? (where $A$ is a complex square matrix).
In the solution: the author proved that $Re\left ( x^{*}Ax \right )> 0$ for all $x\neq 0$
I don't understand how does the inequality: $Re\left ( x^{*}Ax \right )> 0$ for all $x\neq 0$ imply that $A$ is invertible!!
Any help please?