Show that if $v \in \mathbf{R}^p$ then the matrix $A = \left(A_{ij}\right)_{(i,j) \in \llbracket 1,p \rrbracket^2}$ defined by $A = vv^T$ is in $\mathrm{Sym}^+(p)$.
Show that if $v \in \mathbf{R}^p$ then the matrix $A = \left(A_{ij}\right)_{(i,j) \in \llbracket 1,p \rrbracket^2}$ defined by $A = vv^T$ is in $\mathrm{Sym}^+(p)$.