×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Marcus, M., Decomposable symmetrized tensors and an extended LR decomposition theorem, Linear and multilinear algebra, 6, 327-330, (1978) · Zbl 0395.15014
[2] Marcus, M.; Chollet, J., Decomposable symmetrized tensors, Linear and multilinear algebra, 6, 317-326, (1978) · Zbl 0395.15013
[3] Marcus, M.; Chollet, J., Linear groups defined by decomposable tensor equalities, Linear and multilinear algebra, 8, 207-212, (1980) · Zbl 0434.15002
[4] Merris, R., Equality of decomposable symmetrized tensors, Canad. J. math., 27, 1022-1024, (1975) · Zbl 0323.15007
[5] Merris, R.; Dias da Silva, J.A., Generalized Schur functions, J. algebra, 35, 442-447, (1975) · Zbl 0309.15006
[6] de Oliveira, G.N., Generalized matrix functions, (1973), Estudos do Instituto Gulbenkian de Ciência Oeiras, Portugal
[7] de Oliveira, G.N., Interlacing inequalities, Matrix groups, Linear algebra appl., 162-164, 297-307, (1992) · Zbl 0745.15010
[8] de Oliveira, G.N.; Dias da Silva, J.A., Conditions for equality of decomposable symmetric tensors II, Linear algebra appl., 28, 161-176, (1979) · Zbl 0443.15014
[9] de Oliveira, G.N.; Dias da Silva, J.A., Equality of decomposable symmetrized tensors and ∗-matrix groups, Linear algebra appl., 49, 191-219, (1983) · Zbl 0526.15020
[10] de Oliveira, G.N.; Dias da Silva, J.A., On matrix groups defined by certain polynomial identities, Portugal. math., 43, 77-92, (19-5–986)
[11] de Oliveira, G.N.; Santana, Ana P.; Dias da Silva, J.A., Note on the equality of star products, Linear and multilinear algebra, 14, 157-163, (1983) · Zbl 0521.15019
[12] Dias da Silva, J.A., Conditions for equality of decomposable symmetric tensors, Linear algebra appl., 24, 85-92, (1979) · Zbl 0413.15013
[13] Dias da Silva, J.A.; da Purificação Coelho, Ma, Linear groups associated with elements of a group algebra, Linear algebra appl., 94, 165-179, (1987) · Zbl 0629.20019
[14] Dias da Silva, J.A.; da Purificação Coelho, Ma, (λ, G)-critical matrices, Linear algebra appl., 140, 1-11, (1990) · Zbl 0725.15024
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.