2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/23099We derive an estimate of statistical error in calculating the trace of a large matrix by using random vector, and show that {\em random phase vector} gives the results with the smallest statistical error for a given basis set. This result supports use of random phase vectors in the calculation of density of states and linear response functions of large quantum systems.4 pages, RevTex, Further description of real random vectors and self-averaging are addedStatistical MechanicsStrongly Correlated Electronstext