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http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/9183| Title: | On the cardinality of matrices with prescribed rank and partial trace over a finite field |
| Authors: | Balasubramanian, Kumar KAIPA, KRISHNA Khurana, Himanshi Dept. of Mathematics |
| Keywords: | Rank Trace Cardinality Generating function 2024-NOV-WEEK3 TOC-NOV-2024 2025 |
| Issue Date: | Jan-2025 |
| Publisher: | Elsevier B.V. |
| Citation: | Linear Algebra and its Applications, 704, 35-57. |
| 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. |
| URI: | https://doi.org/10.1016/j.laa.2024.10.011 http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/9183 |
| ISSN: | 0024-3795 1873-1856 |
| Appears in Collections: | JOURNAL ARTICLES |
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