The Restricted Isometry Constants (RIC) of a matrix A measures how close to an isometry is the action of A on vectors with few nonzero entries, measured in the `2 norm. Specifically, the upper and lower RIC of a matrix A of size n ×N is the maximum and the minimum deviation from unity (one) of the largest and smallest, respectively, square of singular values of all `N k ́ matrices formed by taki...

In this article, some new results on $M$-matrices, $H$-matrices and their inverse classes are proved. Specifically, we study when a singular $Z$-matrix is an $M$-matrix, convex combinations of $H$-matrices, almost monotone Cholesky factorizations $H$-matrices.