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

KAIPA, KRISHNA; Balasubramanian, Kumar; Khurana, Himanshi

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dc.contributor.author	Balasubramanian, Kumar	en_US
dc.contributor.author	KAIPA, KRISHNA	en_US
dc.contributor.author	Khurana, Himanshi	en_US
dc.date.accessioned	2024-11-22T06:10:46Z
dc.date.available	2024-11-22T06:10:46Z
dc.date.issued	2025-01	en_US
dc.identifier.citation	Linear Algebra and its Applications, 704, 35-57.	en_US
dc.identifier.issn	0024-3795	en_US
dc.identifier.issn	1873-1856	en_US
dc.identifier.uri	https://doi.org/10.1016/j.laa.2024.10.011	en_US
dc.identifier.uri	http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/9183
dc.description.abstract	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.	en_US
dc.language.iso	en	en_US
dc.publisher	Elsevier B.V.	en_US
dc.subject	Rank	en_US
dc.subject	Trace	en_US
dc.subject	Cardinality	en_US
dc.subject	Generating function	en_US
dc.subject	2024-NOV-WEEK3	en_US
dc.subject	TOC-NOV-2024	en_US
dc.subject	2025	en_US
dc.title	On the cardinality of matrices with prescribed rank and partial trace over a finite field	en_US
dc.type	Article	en_US
dc.contributor.department	Dept. of Mathematics	en_US
dc.identifier.sourcetitle	Linear Algebra and its Applications	en_US
dc.publication.originofpublisher	Foreign	en_US