An inverse eigenvalue problem for structured matrices determined by graph pairs

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-07-15 DOI:10.1016/j.laa.2024.07.007

A.H. Berliner , M. Catral , M. Cavers , S. Kim , P. van den Driessche

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引用次数: 0

Abstract

Given a pair of real symmetric matrices $A, B \in R^{n \times n}$ with nonzero patterns determined by the edges of any pair of chosen graphs on n vertices, we consider an inverse eigenvalue problem for the structured matrix $C = [\begin{matrix} A & B \\ I & O \end{matrix}] \in R^{2 n \times 2 n}$ . We conjecture that C can attain any spectrum that is closed under conjugation. We use a structured Jacobian method to prove this conjecture for A and B of orders at most 4 or when the graph of A has a Hamilton path, and prove a weaker version of this conjecture for any pair of graphs with a restriction on the multiplicities of eigenvalues of C.

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由图对决定的结构矩阵的逆特征值问题

给定一对实对称矩阵 A,B∈Rn×n，其非零图案由 n 个顶点上任意一对所选图形的边决定，我们考虑结构矩阵 C=[ABIO]∈R2n×2n的逆特征值问题。我们猜想，C 可以达到任何在共轭作用下封闭的谱。我们使用结构雅各布方法证明了阶最多为 4 或当 A 的图有一条汉密尔顿路径时的 A 和 B 的这一猜想，并证明了对 C 的特征值乘数有限制的任何一对图的这一猜想的较弱版本。

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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.