A bijective proof of generalized Cauchy–Binet, Laplace, Sylvester and Dodgson formulas. Issue 16 (2nd November 2022)

• Record Type: Journal Article
• Authors: Bayat, M.
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 16(2022)
• Page Start: 3220
• Page End: 3230
• Publication Date: 2022-11-02
• Subjects: Determinant of rectangular matrix -- generalized Cauchy–Binet formula -- generalized Laplace's formula -- generalized Sylvester's formula -- generalized Dodgson's formula; 15A15 -- 05A15 -- 05C50; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2020.1832952
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: In this paper, we give the generalization of Cauchy–Binet, Laplace, Sylvester and generalized Dodgson's condensation formulas for the case of rectangular determinants. The proofs are bijective combinatorial proofs similar to that of Zeilberger's paper [Zeilberger D. Dodgson's determinant-evaluation rule proved by TWO-TIMING MEN and WOMEN. Electron J Comb. 1997;4(2):R22; Zeilberger D. A combinatorial approach to matrix algebra. Discrete Math. 1985;56:61–72].