Combined matrix of diagonally equipotent matrices

IF 0.8 Q2 MATHEMATICS Special Matrices Pub Date : 2023-01-01 DOI:10.1515/spma-2023-0101

Rafael Bru, Maria T. Gassó, Isabel Giménez, Máximo Santana, José Scott

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Abstract

Abstract Let C ( A ) = A ∘ A − T {\mathcal{C}}\left(A)=A\circ {A}^{-T} be the combined matrix of an invertible matrix A A , where ∘ \circ means the Hadamard product of matrices. In this work, we study the combined matrix of a nonsingular matrix, which is an H H -matrix whose comparison matrix is singular. In particular, we focus on C ( A ) {\mathcal{C}}\left(A) when A A is diagonally equipotent, and we study whether C ( A ) {\mathcal{C}}\left(A) is an H H -matrix and to which class it belongs. Moreover, we give some properties on the diagonal dominance of these matrices and on their comparison matrices.

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对角等幂矩阵的组合矩阵

摘要设C (A)=A°A−T {\mathcal{C}}\left(A)=A\circ {A}^{-T}是可逆矩阵A A的组合矩阵，其中°\circ表示矩阵的阿达玛积。本文研究了一类非奇异矩阵的组合矩阵，即比较矩阵为奇异的H - H -矩阵。特别地，我们研究了当A A对角等幂时C (A) {\mathcal{C}}\left(A)，并研究了C (A) {\mathcal{C}}\left(A)是否为H -矩阵以及它属于哪个类。此外，我们还给出了这些矩阵及其比较矩阵对角优势性的一些性质。

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.

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