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arXiv · 2111.14840

A Generalized Determinant of Matrices and Applications

Xuesong Lu·Songtao Mao·Zixing Wang·Yuehui Zhang
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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.

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Xuesong Lu, Songtao Mao, Zixing Wang, Yuehui Zhang. 2021-11-29. A Generalized Determinant of Matrices and Applications. https://arxiv.org/abs/2111.14840

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