What does $\mathcal{S}_{++}$ mean?

Question

Context: A multivariate normal distribution has mean $\mu\in \mathbb{R}^p$ and covariance matrix $\Sigma\in \mathcal{S}_{++}^p$. Maybe the $S$ is from 'symmetric' or 'singular', and I know that subscript + means that we only look at the positive part. But double plus?

Answer 1

$\mathcal S^p_{++}$ is the set of all real $p \times p$ symmetric positive definite matrices. $S^p_{+}$ is the set of all real $p \times p$ symmetric positive semidefinite matrices.