Understanding steps of a proof of a positive matrix being symmetric In the solution it's previously proven through weak formulation theorem that if we can show
$<Px,x>=<P^*x,x>$, then a positive matrix is symmetric.
Here is the written proof. We assume that $A$ is a positive matrix.
$<Ax,x>=(Ax)^*x$
$=((Ax)^*x)^*$
$=x^*(Ax)$
$=<x,Ax>$
$=<A^*x,x>$
I have two basic questions about the steps:
I don't understand the first step $<Ax,x>=(Ax)^*x$. How do we end up there?
My second question is is on the second line where it's stated that $(Ax)^*x=((Ax)^*x)^*$. Is this a property of symmetric matrices and why aren't the $x$:es affected by this?

*

*$<Ax,x>=(Ax)^*x$ is the definition of the inner product for two vectors $<x,y> = x^* y$

*$(Ax)^* x$ is a number so that is why is equal to it transpose $(Ax)^*x=((Ax)^*x)^*$
