$A$ is real antisymmetric matrix which satisfies
$$ A^T=-A $$
Prove that
$$ x^TAx=0, \quad x \in \mathbb{R}^n$$
Example of real antisymmetric would be:
$$ A=\begin{bmatrix}0 & -1 \\ 1 & 0 \end{bmatrix} $$
But other than this i dont know where to begin with this.
Now if someone can provide some insight on this that would be much appreciated.
Thanks,
Tuki
Best Answer
Hint: use this$x^TAx=(x^TAx)^T=x^TA^Tx=-x^TAx$.
$x^TAx=(x^TAx)^T$ since $x^TAx$ is a scalar.