Bazı binom katsayılı matrislerin spektral özellikleri
Yükleniyor...
Dosyalar
Tarih
2020
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Kırıkkale Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu tezde öncelikle kaynak özetleri verilerek binom katsayıları, sağa dayalı binom katsayılı matrisler ile bir matrisin determinantı, izi, özdeğeri ve karakteristik polinomunun yanı sıra Fibonacci ve Lucas sayılarının genel yapısı hakkında bilgiler sunulmuştur. Daha sonra sağa dayalı binom katsayılı matrislerin tersiyle farkı olan fark matrislerinin ve toplamı olan toplam matrislerinin determinant, iz, özdeğer, karakteristik polinom ile mod3, mod5 ve mod7 deki karakteristik polinomların yapısında görülen Lucas ve Fibonacci sayılarıyla ilgili bilgiler sunulmuştur.
In this thesis, as first, some informations are introduced by research summaries about determinant, eigenvalue, characteristic polynomial and trace properties of a matrix, beside Lucas and Fibonacci numbers. Theorems about the Lucas and Fibonacci numbers which are seen in the structure of the determinant, trace, eigenvalue, characteristic polynomial of the sum matrix which is the sum of right-justified binomial matrix with it's inverse matrix and also theorems on the generalized polynomials in modulo 3, modulo 5 and modulo 7 are introduced and finally, theorems about the Lucas and Fibonacci numbers which are seen in the structure of the determinant, trace, eigenvalue, characteristic polynomial of the subtract matrix which is the subtract of right-justified binomial matrix with it's inverse matrix and also theorems on the characteristic polynomials in modulo 3, modulo 5 and modulo 7 are introduced.
In this thesis, as first, some informations are introduced by research summaries about determinant, eigenvalue, characteristic polynomial and trace properties of a matrix, beside Lucas and Fibonacci numbers. Theorems about the Lucas and Fibonacci numbers which are seen in the structure of the determinant, trace, eigenvalue, characteristic polynomial of the sum matrix which is the sum of right-justified binomial matrix with it's inverse matrix and also theorems on the generalized polynomials in modulo 3, modulo 5 and modulo 7 are introduced and finally, theorems about the Lucas and Fibonacci numbers which are seen in the structure of the determinant, trace, eigenvalue, characteristic polynomial of the subtract matrix which is the subtract of right-justified binomial matrix with it's inverse matrix and also theorems on the characteristic polynomials in modulo 3, modulo 5 and modulo 7 are introduced.
Açıklama
Anahtar Kelimeler
Matematik, Mathematics
