An inequality for the trace of the product of two symmetric matrices can be used to simplify the proofs of a number of results in multivariate analysis. This is illustrated on two problems: estimating the parametere of a multivariate normal population, and estimating a system of linear functional relationships between the mean vectors of k multivariate normal populations with the same dispersion matrix. A new result is proved for the corresponding structural relationship problem.
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C. M. Theobald (1975) studied this question.
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