ON TRANSINVERSE OF MATRICES AND ITS APPLICATIONS

被引：0

作者：

Hameed, K. shahul ^{[1
]}

Ramakrishnan, K. O. ^{[1
]}

机构：

[1] KMM Govt Womens Coll, Dept Math, POB 670004, Kannur, Kerala, India

来源：

JOURNAL OF ALGEBRAIC SYSTEMS | 2024年 / 12卷 / 01期

关键词：

Gain graph; Signed graph; Graph eigenvalues; Graph Laplacian; BALANCE; GRAPHS;

D O I：

10.22044/JAS.2022.12107.1629

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

. Given a matrix A with the elements from a field of characteristic zero, the transinverse A# of A is defined as the transpose of the matrix obtained by replacing the non-zero elements of A by their inverses and leaving zeros, if any, unchanged. We discuss the properties of this matrix operation in some detail and as an important application, we reinvent the celebrated matrix tree theorem for gain graphs. Characterization of balance in connected gain graphs using its Laplacian matrix becomes an immediate consequence.

引用

页数：14

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