## Connection between a symmetric linear transformation and the unit sphere

There is an interesting correspondence among the quadratic form of a symmetric linear transformation $T:V \mapsto V$on a real Euclidean space,the extreme values of the sphere and the eigenvectors of $T$

Let $Q(x)=(T(x),x)$ be the quadratic form associated with a symmetric linar transformation which maps $V$ into itself,then the set of elements $u$ in V satisfying $\langle u,u \rangle=1$ is called the unit sphere of $V$