Prove that $(S\vec{v})\cdot \vec{u}=\vec{v}\cdot (S\vec{u})$ for symmetrical matrices.
My book asks me to rove that $(S\vec{v})\cdot \vec{u}=\vec{v}\cdot (S\vec{u})$ for all symmetrical matrices S and all vectors $\vec{v}$ and $\vec{u}$.
All I could think of doing is:
$$(S\vec{v})\cdot \vec{u}=(S\vec{v})^T\vec{u}=\vec{v}^TS^T\vec{u}=\vec{v}^T(S\vec{u})=\vec{v}\cdot (S\vec{u})$$
Is there something more to it or is this enough?
Your proof is sufficent. Good job.