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

被引：1
|
作者：
Balasubramanian, Kumar [1 ]
Kaipa, Krishna [2 ]
Khurana, Himanshi [3 ]
机构：
[1] IISER Bhopal, Dept Math, Bhopal 462066, Madhya Pradesh, India
[2] IISER Pune, Dept Math, Pune 411008, Maharashtra, India
[3] Harish Chandra Res Inst, Dept Math, Prayagraj 211019, Uttar Pradesh, India
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2025年 / 704卷
关键词：
Rank; Trace; Cardinality; Generating function; DEGENERATE WHITTAKER MODELS; LINEAR-GROUPS; GAUSS SUMS;
D O I：
10.1016/j.laa.2024.10.011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let F be the finite field of order q and M(n, n, r, F ) be the set of n x n matrices of rank r over the field F . For alpha E F and A E M(n, n, F ), let Z alpha A,r = {X X E M(n, n, r, F ) Tr(AX) AX ) = alpha } . In this article, we solve the problem of determining the cardinality of Z alpha A,r . We also solve the generalization of the problem to rectangular matrices. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
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页码：35 / 57
页数：23
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