Symmetric positive definite matrices, e.g. covariance matrices, are constrained by their symmetry, the strict positivity of the diagonal elements (variance) and the Cauchy-Schwarz inequalities bounding the absolute value of the off-diagonal elements: |Cov(x i x j )|≤[Var(x j )Var(x j )] 1/2 , for all i,j∈{1,…,N}.