grandes-ecoles 2011 QI.A.1

grandes-ecoles · France · centrale-maths2__mp Invariant lines and eigenvalues and vectors Eigenvalue constraints from matrix properties

Let $n \in \mathbb{N}^*$ and $A \in \mathcal{S}_n(\mathbb{R})$. Show that $A$ is positive if and only if all its eigenvalues are positive.

Let $n \in \mathbb{N}^*$ and $A \in \mathcal{S}_n(\mathbb{R})$. Show that $A$ is positive if and only if all its eigenvalues are positive.