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Rank invariance criterion and its application to the unified theory of least squares. (English) Zbl 0694.15003
Necessary and sufficient conditions are established for the matrix product \(AB^-C\) to have its rank invariant with respect to the choice of a generalized inverse \(B^-\) of B. In particular cases, these conditions coincide with results of S. K. Mitra [Sankhyā Ser. A 34, 387-392 (1972; Zbl 0261.15008)]. The results of this paper are also discussed in the context of the unified theory of least squares introduced by C. R. Rao [ibid. 33, 371-394 (1971; Zbl 0236.62048)].
Reviewer: S.L.Campbell

15A09 Theory of matrix inversion and generalized inverses
15A03 Vector spaces, linear dependence, rank, lineability
62J05 Linear regression; mixed models
Full Text: DOI
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