Lets say we have a symmetric positive semi-definite $n\times n$ matrix $\Sigma$, which therefore has a diagonalization $\Sigma=V\Lambda V^T$, where $V$ is an orthogonal matrix (containing the eigenvectors $v_1,...v_n$ of $\Sigma$) and $\Lambda$ is a diagonal matrix (containing the eigenvalues $\lambda_1,...,\lambda_n$ of $\Sigma$).
Could you show me how the following sum of outer products is derived?
$\Sigma=\sum_{i=1}^n \lambda_iv_iv_i^T$