Ranges of Sylvester maps and a minimal rank problem
ELA. The Electronic Journal of Linear Algebra, Tome 20 (2010), pp. 126-135.

Voir la notice de l'article dans Electronic Library of Mathematics

Summary: It is proved that the range of a Sylvester map defined by two matrices of sizes p $\times p$ and q $\times q, respectively,$ plus matrices whose ranks are bounded above, cover all p $\times q$ matrices. The best possible upper bound on the ranks is found in many cases. An application is made to a minimal rank problem that is motivated by the theory of minimal factorizations of rational matrix functions.
Classification : 15A06, 15A99
Mots-clés : Sylvester maps, invariant subspaces, rank 
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     author = {Ran, Andre C.M. and Rodman, Leiba X.},
     title = {Ranges of {Sylvester} maps and a minimal rank problem},
     journal = {ELA. The Electronic Journal of Linear Algebra},
     pages = {126--135},
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     volume = {20},
     year = {2010},
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     url = {https://geodesic-test.mathdoc.fr/item/EEJLA_2010__20__a44/}
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Ran, Andre C.M.; Rodman, Leiba X. Ranges of Sylvester maps and a minimal rank problem. ELA. The Electronic Journal of Linear Algebra, Tome 20 (2010), pp. 126-135. https://geodesic-test.mathdoc.fr/item/EEJLA_2010__20__a44/