一类完全正图的距离矩阵：行列式与逆

IF 0.8 Q2 MATHEMATICS

Special Matrices Pub Date : 2019-06-11 DOI:10.1515/spma-2020-0109

Joyentanuj Das, Sachindranath Jayaraman, Sumit Mohanty

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引用次数: 2

摘要

一个实对称矩阵A如果可以写成某个（不一定是平方的）非负矩阵B的BBt，则称其为完全正图。如果G的每一个非负和半正定的矩阵实现都是完全正矩阵，则简单图G称为完全正图。我们在这篇手稿中的目的是计算一类完全正图的距离矩阵的行列式和逆（当它存在时）。我们计算一个矩阵𝒭 使得一类完全正图的距离矩阵的逆表示为拉普拉斯矩阵、所有1的秩一矩阵和𝒭. 此表达式与树的现有结果类似。我们还提出了一些有趣的光谱性质的主要子矩阵𝒭.

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Distance Matrix of a Class of Completely Positive Graphs: Determinant and Inverse

Abstract A real symmetric matrix A is said to be completely positive if it can be written as BBt for some (not necessarily square) nonnegative matrix B. A simple graph G is called a completely positive graph if every matrix realization of G that is both nonnegative and positive semidefinite is a completely positive matrix. Our aim in this manuscript is to compute the determinant and inverse (when it exists) of the distance matrix of a class of completely positive graphs. We compute a matrix 𝒭 such that the inverse of the distance matrix of a class of completely positive graphs is expressed a linear combination of the Laplacian matrix, a rank one matrix of all ones and 𝒭. This expression is similar to the existing result for trees. We also bring out interesting spectral properties of some of the principal submatrices of 𝒭.

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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.