Random phase vector for calculating the trace of a large matrix

Abstract

We 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 added

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