Let $A \in \mathcal { S } _ { N } ( \mathbb { R } )$. Show that $A \in \mathcal { S } _ { N } ^ { + } ( \mathbb { R } )$ if and only if the eigenvalues of $A$ are all strictly positive real numbers.
Let $A \in \mathcal { S } _ { N } ( \mathbb { R } )$. Show that $A \in \mathcal { S } _ { N } ^ { + } ( \mathbb { R } )$ if and only if the eigenvalues of $A$ are all strictly positive real numbers.