Orbits of pairs of commuting nilpotent matrices : doctoral thesis
Oblak, Polona, matematika
V 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 - dissertation
Publication and manufacture - Ljubljana : [P. Oblak], 2008
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