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Orbits of pairs of commuting nilpotent matrices : doctoral thesisOblak, Polona, matematikaV delu proučujemo Jordanove kanonične forme parov komutirajočih nilpotentnih matrik. (1) Določimo natančno zgornjo mejo za indeks nilpotentnosti matrike, ki komutira z dano matriko ▫$B$▫ v odvisnosti ... od Jordanove kanonične forme matrike ▫$B$▫. (2) Določimo vse možne pare Jordanovih kanoničnih form takšnih nilpotentnih matrik ▫$A$▫ in ▫$B$▫, za katere velja ▫$AB = BA = 0$▫. (3) Karakteriziramo vse matrike, ki jih je mogoče zapisati kot produkt dveh komutirajočih nilpotentnih matrik. (4) Navedemo seznam vseh možnih Jordanovih kanoničnih form nilpotentnih matrik, ki komutirajo z (a) nilpotentno matriko z enim Jordanovim blokom, (b) nilpotentno matriko reda nilpotentnosti 2, (c) ▫$n \times n$▫ nilpotentno matriko, kjer je ▫$n \le 8$▫. (5) Navedemo nekaj možnih Jordanovih kanoničnih form nilpotentnih matrik, ki komutirajo z nilpotentno matriko z dvema Jordanovima blokoma.Type of material - dissertationPublication and manufacture - Ljubljana : [P. Oblak], 2008Language - english, slovenianCOBISS.SI-ID - 14633817
Author
Oblak, Polona, matematika
Other authors
Košir, Tomaž, 1962-
Topics
linearna algebra |
teorija matrik |
komutirajoče matrike |
nilpotentne matrike |
nilpotentne orbite |
Jordanova kanonična forma |
indeks nilpotentnosti |
produkti matrik |
particije |
usmerjeni grafi |
Gansner-Saksov izrek |
linear algebra |
commuting matrices |
nilpotent matrices |
nilpotent orbits |
Jordan canonical form |
index of nilpotency |
mutually annihilating matrices |
products of matrices |
partitions |
directed graphs |
Gasner-Saks theorem
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Database name | Field | Year |
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Oblak, Polona, matematika | 22723 |
Košir, Tomaž, 1962- | 08398 |
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