具有薄谱的中心PSD矩阵是M-矩阵

IF 0.7 4区数学 Q2 Mathematics

Electronic Journal of Linear Algebra Pub Date : 2023-04-17 DOI:10.13001/ela.2023.7051

K. Devriendt

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引用次数: 1

摘要

我们证明了在最大和最小的非零特征值之间的特征值比$\lambda_{\max}/\lambda_{\min}\leq n/(n-2)$的阶为$n$和阶为$n-1$的实的、对称的、中心的(零行和)正半定矩阵具有非正的非对角线项，并且该特征值准则是紧的。结果与矩阵理论和特征值反问题有关，并讨论了在拉普拉斯矩阵中的应用。

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Centered PSD matrices with thin spectrum are M-matrices

We show that real, symmetric, centered (zero row sum) positive semidefinite matrices of order $n$ and rank $n-1$ with eigenvalue ratio $\lambda_{\max}/\lambda_{\min}\leq n/(n-2)$ between the largest and smallest nonzero eigenvalue have nonpositive off-diagonal entries, and that this eigenvalue criterion is tight. The result is relevant in the context of matrix theory and inverse eigenvalue problems, and we discuss an application to Laplacian matrices.

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来源期刊

Electronic Journal of Linear Algebra 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.