具有三角形性质的奇异矩阵的三对角广义逆

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-08-21 DOI:10.1016/j.laa.2025.08.011

A.M. Encinas , K. Kranthi Priya , K.C. Sivakumar

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引用次数: 0

摘要

已知可逆实方阵具有三角形性质当且仅当其逆为三对角矩阵。这一结果具有隐含的重要性，因为非奇异三对角矩阵出现在纯数学和应用数学的各种问题中，因此它们在文献中得到了广泛的研究。然而，这一个案受到的关注相对较少。特别是，很少有人关注这类矩阵的广义逆。本文给出了具有三对角线Moore-Penrose逆或群逆的三角形性质的奇异矩阵的完整描述。相反的陈述也完全正确。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Tridiagonal generalized inverses of singular matrices possessing the triangle property

It is known that an invertible real square matrix has the triangle property if and only if the inverse is a tridiagonal matrix. This result has an implicit importance due to the fact that nonsingular tridiagonal matrices arise in a variety of problems in pure and applied mathematics and for this reason they have been extensively studied in the literature. However, the singular case has received comparatively much lesser attention. In particular, there has been little focus on the generalized inverses of such matrices. In this paper, we provide a complete description of those singular matrices possessing the triangle property to have the tridiagonal Moore-Penrose inverse or group inverse. The converse statements are also completely answered.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.