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Linear spanning sets for matrix spaces


Micheli, Giacomo; Rosenthal, Joachim; Vettori, Paolo (2015). Linear spanning sets for matrix spaces. Linear Algebra and its Applications, 483:309-322.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:26 June 2015
Deposited On:04 Feb 2016 09:59
Last Modified:25 Jun 2017 00:00
Publisher:Elsevier
ISSN:0024-3795
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/j.laa.2015.06.008

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