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On the dimension of the algebra generated by two positive semi-commuting matricesKandić, Marko ; Šivic, Klemen, matematikGerstenhaberjev izrek pravi, da je dimenzija enotske algebre, generirane z dvema komutirajočima ▫$n \times n$▫ matrikama, največ ▫$n$▫. Študiramo analog tega vprašanja za pozitivne matrike s ... pozitivnim komutatorjem. Dokažemo, da je dimenzija algebre, generirane s takima matrikama, največ ▫$\frac{n(n+1)}{2}$▫ in da je ta zgornja meja dosegljiva. Vprašanje obravnavamo tudi v primeru, ko je ena od matrik permutacijska ali pridružena, ali pa sta obe hkrati idempotentni. V teh primerih je zgornja meja bistveno manjša. Posebej, dimenzija algebre, generirane z dvema semi-komutirajočima pozitivnima matrikama, je največ 9. Ta zgornja meja je dosegljiva.Source: Linear algebra and its applications. - ISSN 0024-3795 (Vol. 512, 2017, str. 136-161)Type of material - article, component part ; adult, seriousPublish date - 2017Language - englishCOBISS.SI-ID - 17776985
Author
Kandić, Marko |
Šivic, Klemen, matematik
Topics
Gerstenhaberjev izrek |
semi-komutirajoče matrike |
idealska nerazcepnost |
jordanski blok |
permutacijska matrika |
pridružena matrika |
idempotenti |
Gerstenhaber's theorem |
semi-commuting matrices |
ideal-reducibility |
Jordan block |
permutation matrix |
companion matrix |
idempotents
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Kandić, Marko | 29584 |
Šivic, Klemen, matematik | 28585 |
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