论有限域上具有规定秩和部分迹的矩阵的万有引力

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-10-10 DOI:10.1016/j.laa.2024.10.011

Kumar Balasubramanian , Krishna Kaipa , Himanshi Khurana

引用次数: 0

摘要

对于 α∈F 和 A∈M(n,F)，设ZA,rα={X∈M(n,r,F)|Tr(AX)=α}。在本文中，我们解决了确定 ZA,rα 的万有引力问题。我们还解决了矩形矩阵的一般化问题。

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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On the cardinality of matrices with prescribed rank and partial trace over a finite field

Let F be the finite field of order q and

M (n, r, F)

be the set of

n \times n

matrices of rank r over the field F. For

α \in F

and

A \in M (n, F)

, let

Z_{A, r}^{α} = {X \in M (n, r, F) | Tr (A X) = α} .

In this article, we solve the problem of determining the cardinality of

Z_{A, r}^{α}

. We also solve the generalization of the problem to rectangular matrices.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.