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Abstract:
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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. |