2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118417This paper reviews some characterizations of positive matrices and discusses which lead to useful parametrizations. It is argued that one of them, which we dub the Schur-Constantinescu parametrization is particularly useful. Two new applications of it are given. One shows all block-Toeplitz states are PPT. The other application is to relaxation rates.Submitted for publication to the refereed book ``Mathematics of Quantum Computation and Technology", and is dedicated to the memory of Professor Tiberiu ConstantinescuQuantum Physicstext