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Simetrične matrike : diplomsko delo
Hrašovec, Andreja, 1984-
Simetrične matrike z realnimi elementi so hermitske, zato so unitarno podobne realnim diagonalnim matrikam. Vse njihove lastne vrednosti so realne, prirejene Jordanove kanonične forme so diagonalne ...matrike. V diplomskem delu predstavimo odgovor na naravno vprašanje, ali velja kaj podobnega v primeru, ko so elementi simetričnih matrik kompleksna števila, ki niso vsa realna. Osnovno znanje o hermitskih matrikah podamo v prvem delu. Dopolnimo ga s karakterizacijo matrik, ki so podobne svoji adjungirani matriki. Za simetrične kompleksne matrike obstaja Takagijeva faktorizacija, kar dokažemo v drugem delu. Tu podamo tudi odgovor na zgornje vprašanje, ki je nikalen, saj velja, da je vsaka matrika s kompleksnimi elementi podobna kakšni simetrični matriki s kompleksnimi elementi. Delo zaključimo z opisom tistih kompleksnih matrik, ki so unitarno podobne kakšni kompleksni simetrični matriki.
Type of material - undergraduate thesis
; adult, serious
Publication and manufacture - Maribor : [A. Hrašovec], 2010
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