Remarks on a matrix theorem arising in statistics

Abstract

The following Theorem 1. plays a certain role in statistics and proofs and generalizations have appeared for some time (for algebraic proofs and references see [l], [2]). Although the matrices studied in the theorem are finally shown to be commutative the proofs so far do not go after this fact explicitly. Here a proof wiU be given which links the theorem with commutativity. Further, a recently obtained generalization of the theorem is reproved by reducing it to the special case.

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