论具有双鞍点结构的矩阵的可逆性

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-07-11 DOI:10.1016/j.laa.2024.07.005

Fatemeh P.A. Beik , Chen Greif , Manfred Trummer

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引用次数: 0

摘要

我们为具有双鞍点结构的对称三乘三块矩阵的可逆性建立了必要和充分条件，从而保证了双鞍点系统的唯一可解性。我们考虑了各种情况，包括允许所有对角块都是秩缺陷的情况。在与块的无效性及其核的交集相关的某些条件下，我们得出了一个明确的逆公式。

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On the invertibility of matrices with a double saddle-point structure

We establish necessary and sufficient conditions for invertibility of symmetric three-by-three block matrices having a double saddle-point structure that guarantee the unique solvability of double saddle-point systems. We consider various scenarios, including the case where all diagonal blocks are allowed to be rank deficient. Under certain conditions related to the nullity of the blocks and intersections of their kernels, an explicit formula for the inverse is derived.

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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.