# PRILOG TEORIJI K-CIRKULARNIH MATRICA

 Title: PRILOG TEORIJI K-CIRKULARNIH MATRICA Author: Radičić, Biljana Abstract: In thisdissertation, k-circulantmatricesareconsidered,where k is an arbitrary complexnumber.Themethodforobtainingtheinverseofanon- singular k-circulantmatrix,foranarbitrary k ̸= 0, ispresented,andusing that method,theinverseofanonsingular k-circulantmatrixwithgeometric sequence (witharithmeticsequence)isobtained,foranarbitrary k ̸= 0 (for k = 1). Usingthefullrankfactorizationofàmatrix,theMoore-Penrosein- verseofasingular k-circulantmatrixwithgeometricsequence(witharithme- tic sequence)isdetermined,foranarbitrary k (for k = 1). Foranarbitrary k, the eigenvalues,thedeterminantandtheEuclideannormofa k-circulantma- trix withgeometricsequencei.e.witharithmeticsequencearederived,and boundsforthespectralnormofa k-circulantmatrixwithgeometricsequence are determined.Also, k-circulantmatriceswiththe rstrow (F1; F2; :::;Fn) i.e. (L1;L2; :::;Ln), where Fn i.e. Ln is the nth Fibonaccinumberi.e.Lucas number,areinvestigatedandtheeigenvaluesandtheEuclideannormsof suchmatricesareobtained.BoundsforthespectralnormsoftheHadamard inversesoftheabovematrices,foranarbitrary k ̸= 0, arealsodetermined. Attheendofthisdissertation,theeigenvalues,thedeterminantandbounds for thespectralnormofa k-circulantmatrixwithbinomialcoe cientsare derived,andboundsforthespectralnormoftheHadamardinverseofsuch matrix, foranarbitrary k ̸= 0, aredetermined. URI: http://hdl.handle.net/123456789/4456 Date: 2016

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