Geodesic
A note on preserving the spark of a matrix
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 14 (2015).

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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). 
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     author = {Skrzy\'nski, Marcin},
     title = {A note on preserving the spark of a matrix},
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Skrzyński, Marcin. A note on preserving the spark of a matrix. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 14 (2015). http://geodesic.mathdoc.fr/item/AUPCM_2015_14_a0/