A generalization of weighted versions of the determinant, permanent and the generalized inverse of rectangular matrices

Subject Areas : Linear and multilinear algebra; matrix theory

M. Bayat ¹

1 - Department of Mathematics, Zanjan Branch, Islamic Azad University, P.O. Box 100190, Zanjan, Iran

Received: 2022-07-03 Accepted : 2022-09-26 Published : 2022-09-28

Keywords: The generalized weighted determinant, the generalized weighted permanent, the generalized Cauchy-Binet formula, the generalized Laplace expansion formula, the generalized determinantal inverse, Moore-Penrose weighted inverse,

Abstract :

In this paper, we first generalized the weighted versions of determinants, permanents and the generalized inverses of rectangular matrices. We also investigate some of their algebraic properties. As a by product of the above investigation, we then present a determinantal representation for the general and Moore-Penrose inverses which satisfy on certain conditions. Finally, we give a general algorithm for determining the inverse of some certain class of the rectangular matrices defined based on weighted determinants.

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