2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/109294We use polarization operators known from quantum theory of angular momentum to expand the $N \times N$ dimensional density operators. Thereby, we construct generalized Bloch vectors representing density matrices. We study their properties and derive positivity conditions for any $N$. We also apply the procedure to study Bloch vector space for a qubit and a qutrit.22 pages, 7 figuresQuantum Physicstext