A general determinantal identity of Sylvester type and some applications (Q1319982)
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scientific article; zbMATH DE number 553955
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A general determinantal identity of Sylvester type and some applications |
scientific article; zbMATH DE number 553955 |
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A general determinantal identity of Sylvester type and some applications (English)
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4 December 1994
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Sylvester's classical determinantal identity can be interpreted as an extension of Leibniz's definition of the determinant of the matrix via Muir's law of expensible minors. Papers of \textit{R. A. Brualdi} and \textit{H. Schneider} [Linear Algebra and Appl. 52-53, 769-791 (1983; Zbl 0533.15007)] have extended Muir's law. These extensions inspired \textit{G. Mühlbach} and \textit{M. Gasca} [Linear Algebra Appl. 66, 221-234 (1985; Zbl 0576.15005)] to corresponding generalizations of Sylvester's identities. In the present paper these developments are simplified and freed from certain index restrictions. The reviewer refers the interested reader also to the very interesting developments of \textit{B. Leclerc} [On identities satisfied by minors of a matrix. Adv. Math. 100, 101-132 (1993)].
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Muir's law of expensible minors
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Sylvester determinant identity
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