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).
@article{bwmeta1.element.doi-10_1515_aupcsm-2015-0005,
author = {Marcin Skrzy\'nski},
title = {A note on preserving the spark of a matrix},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
volume = {14},
year = {2015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_aupcsm-2015-0005}
}
Marcin Skrzyński. A note on preserving the spark of a matrix. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 14 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_aupcsm-2015-0005/