 Covariance matrix

For a random vector $X$ with finite second moments, its covariance matrix isIt is positive semidefinite, and the variance of $a^{T}X$ is $a^T\mathrm{cov}(X)a$.

A covariance matrix is a square matrix that captures the covariance between multiple random variables. It is a key concept in statistics, probability theory, and multivariate data analysis. Each element in the covariance matrix represents the covariance between two variables.