On the Properties of r-Circulant Matrices Involving Generalized Fermat Numbers
-circulant matrices have applied in numerical computation, signal processing, coding theory, etc. In this study, our main goal is to investigate the r-circulant matrices of generalized Fermat numbers which are shown by We obtain the eigenvalues, determinants, sum identity of matrices. Also we find...
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| Language: | English |
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Sakarya University
2023-10-01
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| Series: | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/3073740 |
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| author | Engin Özkan Engin Eser Bahar Kuloǧlu |
| author_facet | Engin Özkan Engin Eser Bahar Kuloǧlu |
| author_sort | Engin Özkan |
| collection | DOAJ |
| description | -circulant matrices have applied in numerical computation, signal processing, coding theory, etc. In this study, our main goal is to investigate the r-circulant matrices of generalized Fermat numbers which are shown by We obtain the eigenvalues, determinants, sum identity of matrices. Also we find upper and lower bounds for the spectral norms of generalized Fermat r-circulant matrices. Beside these, we present 〖GR〗_(a,b,r)^* matrix in the form of the Hadamard product of two matrices as 〖GR〗_(a,b,r)^*=A.B. In addition, we get the right and skew-right circulant matrices for . Finally, we examine their different norms (Spectral and Euclidean) and limits for matrix norms. |
| format | Article |
| id | doaj-art-f988edb1d3ba4342b515c480b4a98504 |
| institution | Kabale University |
| issn | 2147-835X |
| language | English |
| publishDate | 2023-10-01 |
| publisher | Sakarya University |
| record_format | Article |
| series | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
| spelling | doaj-art-f988edb1d3ba4342b515c480b4a985042024-12-23T08:15:41ZengSakarya UniversitySakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi2147-835X2023-10-0127595696410.16984/saufenbilder.128057228On the Properties of r-Circulant Matrices Involving Generalized Fermat NumbersEngin Özkan0https://orcid.org/0000-0002-4188-7248Engin Eser1https://orcid.org/0000-0001-5965-4162Bahar Kuloǧlu2https://orcid.org/0000-0001-7624-8270ERZINCAN BINALI YILDIRIM UNIVERSITYERZINCAN BINALI YILDIRIM UNIVERSITYERZİNCAN ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ-circulant matrices have applied in numerical computation, signal processing, coding theory, etc. In this study, our main goal is to investigate the r-circulant matrices of generalized Fermat numbers which are shown by We obtain the eigenvalues, determinants, sum identity of matrices. Also we find upper and lower bounds for the spectral norms of generalized Fermat r-circulant matrices. Beside these, we present 〖GR〗_(a,b,r)^* matrix in the form of the Hadamard product of two matrices as 〖GR〗_(a,b,r)^*=A.B. In addition, we get the right and skew-right circulant matrices for . Finally, we examine their different norms (Spectral and Euclidean) and limits for matrix norms.https://dergipark.org.tr/tr/download/article-file/3073740fermat numbergeneralized fermat numbersnorm (spectral and euclidean)eigenvaluescirculant matrices |
| spellingShingle | Engin Özkan Engin Eser Bahar Kuloǧlu On the Properties of r-Circulant Matrices Involving Generalized Fermat Numbers Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi fermat number generalized fermat numbers norm (spectral and euclidean) eigenvalues circulant matrices |
| title | On the Properties of r-Circulant Matrices Involving Generalized Fermat Numbers |
| title_full | On the Properties of r-Circulant Matrices Involving Generalized Fermat Numbers |
| title_fullStr | On the Properties of r-Circulant Matrices Involving Generalized Fermat Numbers |
| title_full_unstemmed | On the Properties of r-Circulant Matrices Involving Generalized Fermat Numbers |
| title_short | On the Properties of r-Circulant Matrices Involving Generalized Fermat Numbers |
| title_sort | on the properties of r circulant matrices involving generalized fermat numbers |
| topic | fermat number generalized fermat numbers norm (spectral and euclidean) eigenvalues circulant matrices |
| url | https://dergipark.org.tr/tr/download/article-file/3073740 |
| work_keys_str_mv | AT enginozkan onthepropertiesofrcirculantmatricesinvolvinggeneralizedfermatnumbers AT engineser onthepropertiesofrcirculantmatricesinvolvinggeneralizedfermatnumbers AT baharkuloglu onthepropertiesofrcirculantmatricesinvolvinggeneralizedfermatnumbers |