<abstract xmlns="http://www.w3.org/1999/xhtml">

 Let Mm×n(F) be the vector space of all m×n matrices over a field F. In the case where m ≥ n, char(F) ≠ 2 and F has at least five elements, we give a complete characterization of linear maps Φ: Mm×n(F) → Mm×n(F) such that spark(Φ(A)) = spark(A) for any A ∈Mm×n(F). 
</abstract>

Let Mm×n(F) be the vector space of all m×n matrices over a field F. In the case where m ≥ n, char(F) ≠ 2 and F has at least five elements, we give a complete characterization of linear maps Φ: Mm×n(F) → Mm×n(F) such that spark(Φ(A)) = spark(A) for any A ∈Mm×n(F).

A note on preserving the spark of a matrix

Institute of Mathematics Cracow University of Technology ul. Warszawska 24 31-155 Kraków Poland

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

{"article-title":"A note on preserving the spark of a matrix"}

Let Mm×n(F) be the vector space of all m×n matrices over a field F. In the case where m ≥ n, char(F) ≠ 2 and F has at least five elements, we give a complete...

A note on preserving the spark of a matrix

Published Online: Dec 30, 2015

Page range: 63 - 67

Received: Oct 12, 2014

DOI: https://doi.org/10.1515/aupcsm-2015-0005

© by Marcin Skrzyński

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.