Generalizations of Sylvester's determinantal identity
Numerical Analysis
2015-03-03 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1503.00519,
title = {Generalizations of Sylvester's determinantal identity},
author = {Anna Karapiperi and Michela Redivo-Zaglia and Maria Rosaria Russo},
journal= {arXiv preprint arXiv:1503.00519},
year = {2015}
}