Let $u$ be an endomorphism of $\mathbb{R}^n$. Show that $u$ is self-adjoint positive definite if and only if its matrix in any orthonormal basis belongs to $\mathcal{S}_n^{++}(\mathbb{R})$.
Let $u$ be an endomorphism of $\mathbb{R}^n$. Show that $u$ is self-adjoint positive definite if and only if its matrix in any orthonormal basis belongs to $\mathcal{S}_n^{++}(\mathbb{R})$.