Lengths of quasi-commutative pairs of matrices
| dc.contributor.author | Guterman, Alexander E. | |
| dc.contributor.author | Markova, Olga V. | |
| dc.contributor.author | Mehrmann, Volker | |
| dc.date.accessioned | 2021-12-17T10:13:35Z | |
| dc.date.available | 2021-12-17T10:13:35Z | |
| dc.date.issued | 2015-06-18 | |
| dc.description.abstract | In this paper we discuss some partial solutions of the length conjecture which describes the length of a generating system for matrix algebras. We consider mainly the algebras generated by two matrices which are quasi-commuting. It is shown that in this case the length function is linearly bounded. We also analyze which particular natural numbers can be realized as the lengths of certain special generating sets and prove that for commuting or product-nilpotent pairs all possible numbers are realizable, however there are non-realizable values between lower and upper bounds for the other quasi-commuting pairs. In conclusion we also present several related open problems. | en |
| dc.identifier.issn | 2197-8085 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/15850 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-14623 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 510 Mathematik | en |
| dc.subject.other | finite-dimensional algebras | en |
| dc.subject.other | lengths of sets and algebras | en |
| dc.subject.other | quasi-commuting matrices | en |
| dc.title | Lengths of quasi-commutative pairs of matrices | en |
| dc.type | Research Paper | en |
| dc.type.version | submittedVersion | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |
| tub.series.issuenumber | 2015, 09 | en |
| tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
| tub.subject.msc2000 | 15A30 Algebraic systems of matrices | en |
| tub.subject.msc2000 | 16S50 Endomorphism rings; matrix rings | en |
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