Ranges of Sylvester maps and a minimal rank problem

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Andre C. M. Ran
Leiba X. Rodman


It is proved that the range of a Sylvester map defined by two matrices of sizes p × p and q × q, respectively, plus matrices whose ranks are bounded above, cover all p × 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.

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