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

Journal of Linear and Topological Algebra

دوره 11، شماره 03، آذر 2022، صفحه 189-203   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.30495/jlta.2022.695232

نویسنده

M. Bayat^*

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

چکیده

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.

کلیدواژه‌ها

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

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