I know that the property $\langle u, v \rangle = \overline{\langle v, u \rangle}$ for inner product holds.
I have a matrix $A$, such that,
$\langle Ax, x \rangle = -\langle x, Ax \rangle$ i.e.
$\langle x, Ax \rangle = -\overline{\langle x, Ax \rangle}$.
What does this imply about $Ax$ and $x$?
I need to show that $\langle Ax, x \rangle = 0$, which is actually valid for any $A = -A^T$, which I verified using sample matrices, but cannot verify in general. Can anyone help?
Thanks.