Show the set of symetric postive semidefinite is a cone in $\mathbb{R}^{n\times n}$ [closed]
Solution 1:
$M\in\mathbb{S}_{+}^{n}$
$x^T Mx\geq 0 \,\forall x\in\Bbb R^n$
$\lambda x^T Mx\geq 0$
$x^T (\lambda M) x\geq 0$
$\lambda M\in\mathbb{S}_{+}^{n}$
Show the set of symetric postive semidefinite is a cone in $\mathbb{R}^{n\times n}$ [closed]
Solution 1:
$M\in\mathbb{S}_{+}^{n}$
$x^T Mx\geq 0 \,\forall x\in\Bbb R^n$
$\lambda x^T Mx\geq 0$
$x^T (\lambda M) x\geq 0$
$\lambda M\in\mathbb{S}_{+}^{n}$