A trace bound for integer-diagonal positive semidefinite matrices

IF 0.8 Q2 MATHEMATICS

Special Matrices Pub Date : 2020-01-01 DOI:10.1515/spma-2020-0002

Lon H. Mitchell

引用次数: 1

Abstract

Abstract We prove that an n-by-n complex positive semidefinite matrix of rank r whose graph is connected, whose diagonal entries are integers, and whose non-zero off-diagonal entries have modulus at least one, has trace at least n + r − 1.

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整数对角半正定矩阵的迹界

摘要我们证明了一个秩为r的n乘n复半正定矩阵，其图是连通的，其对角项是整数，其非零非对角项的模至少为1，其迹至少为n+r-1。

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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来源期刊

Special Matrices MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

8 weeks

期刊介绍： Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.