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Generalizations of Sylvester's determinantal identity

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arxiv 1503.00519 v1 pith:XDZYLWSB submitted 2015-03-02 math.NA cs.NA

Anna Karapiperi , Michela Redivo-Zaglia , Maria Rosaria Russo This is my paper · ORCID
classification math.NAcs.NA
keywords sylvesteridentitydeterminantdeterminantalgascageneralizationgeneralizationsmatrix
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In this paper we deal with the noteworthy Sylvester's determinantal identity and some of its generalizations. We report the formulae due to Yakovlev, to Gasca, Lopez--Carmona, Ramirez, to Beckermann, Gasca, M\"uhlbach, and to Mulders in a unified formulation which allows to understand them better and to compare them. Then, we propose a different generalization of Sylvester's classical formula. This new generalization expresses the determinant of a matrix in relation with the determinant of the bordered matrices obtained adding more than one row and one column to the original matrix. Sylvester's identity is recovered as a particular case.

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