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Zveza med posplošenimi inverzi in delno urejenostjo na matrikah : magistrsko deloSiladi, Nataša, 1981-Najprej bomo predstavili osnovne pojme povezane z matrikami in rezultate povezane s temi pojmi, ki jih bomo potrebovali v nadaljevanju. Pri delu z matrikami nam je velikokrat v pomoč, če za dano ... matriko poznamo njen inverz. Če je matrika ▫$A$▫ kvadratna in nesingularna, potem obstaja inverzna matrika ▫$A^{-1}$▫, tako da je ▫$AA^{-1}=A^{-1}A=I$▫. Ker vsaka matrika nima inverza, lahko za dano matriko poiščemo matriko, ki ima podobne lastnosti kot inverzna matrika. Zato za singularne kvadratne in tudi za pravokotne matrike definiramo posplošeni inverz matrike. V drugem poglavju bomo predstavili različne posplošene inverze matrik in njihove lastnosti. Na matrikah lahko definiramo tudi več različnih delnih urejenosti, ki imajo pomembne interpretacije v različnih vejah znanosti. V tretjem poglavju bomo predstavili nekaj pomembnejših delnih urejenosti na matrikah, kot so delna urejenost odštevanje ranga, zvezdica delna urejenost, minus delna urejenost, ... Znano je, da obstajajo različne povezave med posplošenimi inverzi in delnimi urejenostmi. Predstavili bomo enotno teorijo. S pomočjo preslikave ▫${\cal G}$▫, ki slika iz prostora matrik ▫$M_{m,n}$▫ v potenčno množico matrik ▫${\cal P}(M_{n,m})$▫, pri čemer preslikava ▫${\cal G}$▫ vsaki matriki ▫$A$▫ priredi neko podmnožico njenih posplošenih inverzov, sta definirani relaciji ekvivalentni minus delni urejenosti oz. zvezdica delni urejenosti. V četrtem poglavju bomo predstavili lastnosti preslikave ▫${\cal G}$▫ in podali pogoje, da bo prej omenjena relacija relacija delne urejenosti. Pogledali bomo tudi razširjeno preslikavo ▫${\cal G}$▫ in njej inverzno preslikavo ▫${\cal G}^{-1}$▫.Type of material - master's thesisPublication and manufacture - Ljubljana : [N. Siladi], 2009Language - slovenianCOBISS.SI-ID - 15106137
Author
Siladi, Nataša, 1981-
Other authors
Dolinar, Gregor, 11.08.1971-
Topics
matrične algebre |
posplošeni inverz |
Moore-Penroseov inverz |
delna urejenost |
minus delna urejenost |
matrix algebra |
generalized inverse |
Moore-Penrose inverse |
partial order |
minus order
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Library | Call number – location, accession no. ... | Copy status |
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FMF, Mathematical Library, Lj. | Skladišče-Jadranska 21 11052/44 |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Siladi, Nataša, 1981- | ![]() |
Dolinar, Gregor, 11.08.1971- | 18750 |
Source: Personal bibliographies
and: SICRIS
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