Hemen-hemen Hilbert-Smith matrislerinin karakterizasyonu
The Characterization of the almost Hilbert-Smith matrices
- Tez No: 106183
- Danışmanlar: PROF. DR. DURSUN TAŞÇI
- Tez Türü: Yüksek Lisans
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: The Almost Hilbert-Smith matrix, The GCD matrix, Euler's totient function, factor closed set, greatest common divisor closed set IV
- Yıl: 2001
- Dil: Türkçe
- Üniversite: Selçuk Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Matematik Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 52
Özet
ABSTRACT PhD Thesis THE CHARACTERIZATION OF THE ALMOST HILBERT-SMITH MATRICES Ercan ALTJJMIŞIK Selçuk University Graduate School of Natural and Applied Sciences Department of Mathematics Supervisor Prof. Dr. Dursun TAŞÇI 2001, 47 pages Jury: Prof. Dr. Hüseyin ALTINDİŞ Prof. Dr. Hasan ŞENAY Prof. Dr. Ali SİNAN Prof. Dr. Dursun TAŞÇI Doç. Dr. Durmuş BOZKURT ((' 'V\ In this study, a matrix [s]=(sğ)x = ^~ has been defined and called the ^ ij ) almost Hubert-Smith matrix. Firstly, the structure of the matrix [s] has been investigated, the determinant and the entries of the inverse of [s] have been obtained in terms of some special arithmetical functions. The structure of the almost Hilbert-Smith matrix, which is defined as [S]= (sğ)= " J on a set S = {xi,x2,...,xn} of positive V x*xj J integers, has been investigated. The determinant and the entries of the inverse of the almost Hilbert-Smith matrix on S have been obtained in terms of some special arithmetical functions in case S is factor closed and greatest common divisor closed. In the last section a generalization of the almost Hilbert-Smith matrix has been given as (I V^\ where r e Z and the structure of this matrix has been H-to- r r XiXj investigated. The determinant of this matrix has been calculated in terms of Jordan's totient function, that is a generalization of Euler's totient function. Finally the entries of the inverse of this matrix have been calculated in terms of Jordan's totient and Möbius function.
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