Rank invariance criterion and its application to the unified theory of least squares (Q908988)
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scientific article; zbMATH DE number 4136122
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rank invariance criterion and its application to the unified theory of least squares |
scientific article; zbMATH DE number 4136122 |
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Rank invariance criterion and its application to the unified theory of least squares (English)
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1990
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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 \textit{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 \textit{C. R. Rao} [ibid. 33, 371-394 (1971; Zbl 0236.62048)].
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rank
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statistics
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matrix product
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generalized inverse
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theory of least squares
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