English

A Generalized Determinant of Matrices and Applications

Classical Analysis and ODEs 2021-12-01 v1

Abstract

A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping multiplication formula and partly keeping the Cauchy-Binet's formula. As applications of the new theory, the generalized Cramer's rule and the generalized oriented volume are obtained.

Keywords

Cite

@article{arxiv.2111.14840,
  title  = {A Generalized Determinant of Matrices and Applications},
  author = {Xuesong Lu and Songtao Mao and Zixing Wang and Yuehui Zhang},
  journal= {arXiv preprint arXiv:2111.14840},
  year   = {2021}
}

Comments

11 pages

R2 v1 2026-06-24T07:56:25.048Z