SOME DECOMPOSITIONS OF MATRIX VARIANCES
Abstract: When
is a density matrix and
are self-adjoint operators, then the standard
variance is a
matrix:

The
main result in this work is that there are projections

such that

with

and

and

. In a previous
paper only the

case was included and the relevance is motivated by the paper [8].
2000 AMS Mathematics Subject Classification: Primary: 62J10; Secondary:
62F30.
Keywords and phrases: Density matrix, variance, covariance, decomposition,
projections.Marekċ Częysóołwski