Micheli, Giacomo; Rosenthal, Joachim; Vettori, Paolo (2015). Linear spanning sets for matrix spaces. Linear Algebra and its Applications, 483:309-322.
Necessary and sufficient conditions are given on matrices $\mathit{A}$, $\mathit{B}$ and $\mathit{S}$, having entries in some field $\mathbb{F}$ and suitable dimensions, such that the linear span of the terms $\mathit{A}^i \mathit{SB}^j$ over $\mathbb{F}$ is equal to the whole matrix space. This result is then used to determine the cardinality of subsets of $\mathbb{F}[\mathit{A}]\mathit{S} \mathbb{F}[\mathit{B}]$ when $\mathbb{F}$ is a $\mathbf{finite}$ field.
Necessary and sufficient conditions are given on matrices $\mathit{A}$, $\mathit{B}$ and $\mathit{S}$, having entries in some field $\mathbb{F}$ and suitable dimensions, such that the linear span of the terms $\mathit{A}^i \mathit{SB}^j$ over $\mathbb{F}$ is equal to the whole matrix space. This result is then used to determine the cardinality of subsets of $\mathbb{F}[\mathit{A}]\mathit{S} \mathbb{F}[\mathit{B}]$ when $\mathbb{F}$ is a $\mathbf{finite}$ field.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Algebra and Number Theory
Physical Sciences > Numerical Analysis Physical Sciences > Geometry and Topology Physical Sciences > Discrete Mathematics and Combinatorics |
| Language: | English |
| Date: | 26 June 2015 |
| Deposited On: | 04 Feb 2016 09:59 |
| Last Modified: | 15 Nov 2023 02:37 |
| Publisher: | Elsevier |
| ISSN: | 0024-3795 |
| OA Status: | Hybrid |
| Free access at: | Publisher DOI. An embargo period may apply. |
| Publisher DOI: | https://doi.org/10.1016/j.laa.2015.06.008 |
Micheli, Giacomo