Question: Let $Omega$ be a $K times K$ variance matrix. (a) Show that $Omega$ is positive semidefinite for all $w in mathbb{R}^K$, $w'Omega w ge 0$.
Let $\Omega$ be a $K \times K$ variance matrix.
(a) Show that $\Omega$ is positive semidefinite for all $w \in \mathbb{R}^K$, $w'\Omega w \ge 0$.
(b) Show that $\Omega$ is nonsingular if and only if $\Omega$ is positive definite.
(c) Show that $\Omega^{-1}$ is positive definite if $\Omega$ is nonsingular.
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