A parameterization of the density operator, a coherence vector representation, which uses a basis of orthogonal, traceless, Hermitian matrices is discussed. Using this parameterization we find the region of permissible vectors which represent a density operator. The inequalities which specify the region are shown to involve the Casimir invariants of the group. In particular cases, this allows the determination of degeneracies in the spectrum of the operator. The identification of the Casimir invariants also provides a method of constructing quantities which are invariant under local unitary operations. Several examples are given which illustrate the constraints provided by the positivity requirements and the utility of the coherence vector parameterization.

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Three groups of people ranging in age from 64 to 88 years performed tasks of word generation, paired-associate recall, and free and cued recall. The groups differed in socioeconomic status, verbal intelligence, and apparent levels of daily activity. A fourth group, consisting of young undergraduates, was also tested. Results showed that whereas there were age-related differences in some tests, these age differences were strongly modulated by characteristics of the participants and characteristics of the tasks. The findings are discussed in a contextualist framework.