arXiv 1707.092392017-07-28math.RA

Some additive decompositions of $\mathbb{K}$-regular matrices

Alberto Dolcetti, Donato Pertici

英文摘要：

Under suitable hypotheses on the ground field and on the matrix $M$, we discuss existence, uniqueness and properties of some additive decompositions of $M$ and of its image through a convergent series.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Vector-Circulant Matrices over Finite Fields and Related Codes

A vector-circulant matrix is a natural generalization of the classical circulant matrix and has applications in constructing additive codes. This article formulates the concept of a vector-circulant matrix over finite fields and gives an algebraic characterization for this kind of matrix. Finally, a construction of additive codes with vector-circulant based over $\mathbb{F}_4$ is given together with some examples of good half-rate additive codes.

2014-08-09math.RA

秩- $k$矩阵上的交换映射

Commuting maps on rank-$k$ matrices

$n\geq2$是一个自然数。设$M_n(\mathbb{K})$是域$\mathbb{K}$上所有$n \times n$矩阵的环。固定自然数$k$满足$1<k\leq n$。在对$\mathbb{K}$的一个温和的技术假设下，我们将证明，加性映射$G:M_n(\mathbb{K})\to M_n(\mathbb{K})$使得对于每个秩- $k$矩阵$x\in M_n(\mathbb{K})$的$[G(x),x]=0$具有形式$λx + μ(x)$，其中$λ\in Z$、$μ:M_n(\mathbb{K})\to Z$和$Z$代表$M_n(\mathbb{K})$的中心。此外，我们将看到一个例子，存在加法映射，使得对于所有不具有$λx + μ(x)$形式的秩为1的矩阵，$[G(x),x]=0$。我们还将讨论$m$ -可加性的情况。

2012-12-03math.RA

Banach代数中群逆的加性结果

Additive results of group inverses in Banach algebras

本文研究Banach代数中两个群可逆元素之和的群逆表示，并将所得结果应用于分块复矩阵，从而得到某些分块复矩阵的群可逆性。

2024-02-24math.FAmath.RA

矩阵的永久秩的加法保持算子

Additive preservers of permanent rank

本文刻画保持永久秩1矩阵的加法变换，在满射或双向保持的条件下，证明其为对角矩阵乘法、置换矩阵乘法、转置及基域单射自同态的复合。

2026-08-03math.COmath.RA

New Representation of Drazin Inverse for Block complex matrices

We present a new formula for the Drazin inverse of the sum of two complex matrices under weaker conditions with perturbations. By using this additive results, we establish new representations for the Drazin inverse of 2 \times 2 block complex matrix under certain new conditions involving perturbations.

2021-07-07math.RA

关于有限自由位置中的矩阵

On matrices in finite free position

本文研究加法与乘法有限自由位置中的方阵对，通过特征多项式与有限自由卷积的关系刻画互补矩阵对的代数集格，涵盖对角、三角及标量矩阵等典型情形。

2025-06-23math.PRmath.RA

更多相关论文收起更多论文

Some Explicit Solutions of the Additive Deligne-Simpson Problem and Their Applications (Preprint)

In this paper we construct three infinite series and two extra triples of complex matrices B, C, and A=B+C of special spectral types associated to C. Simpson's classification in his paper ``Products of Matrices'' and a classification of multiple flag varieties with finitely many orbits of the diagonal action of the general linear group by P. Magyar, J. Weyman, and A. Zelevinsky. This enables us to construct Fuchsian systems of differential equations which generalize the hypergeometric equation of Gauss-Riemann. In a sense, they are the closest relatives of the famous equation, because their tr…

2002-04-27math.RA

Local derivations on associative and Jordan matrix algebras

In the present paper we prove that every additive (not necessarily homogenous) local inner derivation on the algebra of matrices over an arbitrary field is an inner derivation, and every local inner derivation on the ring of matrices over a finite ring generated by the identity element or the ring of integers is an inner derivation. We also prove that every additive local inner derivation on the Jordan algebra of symmetric matrices over an arbitrary field is a derivation, and every local inner derivation on the Jordan ring of symmetric matrices over a finite ring generated by the identity elem…

2019-01-25math.OAmath.RA

几乎严格符号正矩阵的组合矩阵

Combined matrices of almost strictly sign regular matrices

本文研究了几乎严格符号正（ASSR）矩阵的组合矩阵，证明了在不可约条件下其零和非零元素模式被保留，无此条件时I型和II型阶梯模式仍被保留。

2024-02-02math.COmath.RA

三角矩阵的定律

Laws for triangular matrices

School of Mathematics and Statistics, Lanzhou University（兰州大学数学与统计学院）；Department of Mathematics and Statistics, Chongqing Technology and Business University（重庆工商大学数学与统计学院）；Institute of Natural Sciences and Mathematics, Ural Federal University（乌拉尔联邦大学自然科学与数学研究所）

该研究探讨域上及含0和1的加法幂等半环上三角矩阵幺半群的恒等式，发现部分此类恒等式无有限公理化的新情况。

2026-09-01math.GRmath.LOmath.RA

A characterization of $(\mathcal{I}, \mathcal{J})$-regular matrices

Let $\mathcal{I},\mathcal{J}$ be two ideals on $\mathbf{N}$ which contain the family $\mathrm{Fin}$ of finite sets. We provide necessary and sufficient conditions on the entries of an infinite real matrix $A=(a_{n,k})$ which maps $\mathcal{I}$-convergent bounded sequences into $\mathcal{J}$-convergent bounded sequences and preserves the corresponding ideal limits. The well-known characterization of regular matrices due to Silverman--Toeplitz corresponds to the case $\mathcal{I}=\mathcal{J}=\mathrm{Fin}$. Lastly, we provide some applications to permutation and diagonal matrices, which extend se…

2021-05-21math.FAmath.GNmath.RA