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Semigroups defined by generalized Schur functions. (English) Zbl 0871.15005
The author proves that the characterization of the singular matrices $$A$$ satisfying (1) $$d^H_l (AX)= d^H_l (XA)$$ $$\forall X$$ can be reduced to that of matrices satisfying (2) $$d_l^H(AX) =0$$ $$\forall X$$, where $$d^H_l$$ is a Schur function. Some partial results on the characterization of (2) are obtained.

##### MSC:
 15A15 Determinants, permanents, traces, other special matrix functions
##### Keywords:
singular matrices; Schur function; characterization
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##### References:
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