One Type of Symmetric Matrix with Harmonic Pell Entries, Its Inversion, Permanents and Some Norms
The Pell numbers, named after the English diplomat and mathematician John Pell, are studied by many authors. At this work, by inspiring the definition harmonic numbers, we define harmonic Pell numbers. Moreover, we construct one type of symmetric matrix family whose elements are harmonic Pell number...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/5/539 |
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| author | Seda Yamaç Akbiyik Mücahit Akbiyik Fatih Yilmaz |
| author_facet | Seda Yamaç Akbiyik Mücahit Akbiyik Fatih Yilmaz |
| author_sort | Seda Yamaç Akbiyik |
| collection | DOAJ |
| description | The Pell numbers, named after the English diplomat and mathematician John Pell, are studied by many authors. At this work, by inspiring the definition harmonic numbers, we define harmonic Pell numbers. Moreover, we construct one type of symmetric matrix family whose elements are harmonic Pell numbers and its Hadamard exponential matrix. We investigate some linear algebraic properties and obtain inequalities by using matrix norms. Furthermore, some summation identities for harmonic Pell numbers are obtained. Finally, we give a MATLAB-R2016a code which writes the matrix with harmonic Pell entries and calculates some norms and bounds for the Hadamard exponential matrix. |
| first_indexed | 2024-03-09T05:32:16Z |
| format | Article |
| id | doaj.art-6235ffbdfb794d2abd04a043b141f878 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:32:16Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6235ffbdfb794d2abd04a043b141f8782023-12-03T12:31:53ZengMDPI AGMathematics2227-73902021-03-019553910.3390/math9050539One Type of Symmetric Matrix with Harmonic Pell Entries, Its Inversion, Permanents and Some NormsSeda Yamaç Akbiyik0Mücahit Akbiyik1Fatih Yilmaz2Department of Computer Engineering, Istanbul Gelisim University, 34310 Istanbul, TurkeyDepartment of Mathematics, Beykent University, 34520 Istanbul, TurkeyDepartment of Mathematics, Ankara Hacı Bayram Veli University, 06900 Ankara, TurkeyThe Pell numbers, named after the English diplomat and mathematician John Pell, are studied by many authors. At this work, by inspiring the definition harmonic numbers, we define harmonic Pell numbers. Moreover, we construct one type of symmetric matrix family whose elements are harmonic Pell numbers and its Hadamard exponential matrix. We investigate some linear algebraic properties and obtain inequalities by using matrix norms. Furthermore, some summation identities for harmonic Pell numbers are obtained. Finally, we give a MATLAB-R2016a code which writes the matrix with harmonic Pell entries and calculates some norms and bounds for the Hadamard exponential matrix.https://www.mdpi.com/2227-7390/9/5/539harmonic pell numberspectral normhadamard inversepermanentdeterminant |
| spellingShingle | Seda Yamaç Akbiyik Mücahit Akbiyik Fatih Yilmaz One Type of Symmetric Matrix with Harmonic Pell Entries, Its Inversion, Permanents and Some Norms Mathematics harmonic pell number spectral norm hadamard inverse permanent determinant |
| title | One Type of Symmetric Matrix with Harmonic Pell Entries, Its Inversion, Permanents and Some Norms |
| title_full | One Type of Symmetric Matrix with Harmonic Pell Entries, Its Inversion, Permanents and Some Norms |
| title_fullStr | One Type of Symmetric Matrix with Harmonic Pell Entries, Its Inversion, Permanents and Some Norms |
| title_full_unstemmed | One Type of Symmetric Matrix with Harmonic Pell Entries, Its Inversion, Permanents and Some Norms |
| title_short | One Type of Symmetric Matrix with Harmonic Pell Entries, Its Inversion, Permanents and Some Norms |
| title_sort | one type of symmetric matrix with harmonic pell entries its inversion permanents and some norms |
| topic | harmonic pell number spectral norm hadamard inverse permanent determinant |
| url | https://www.mdpi.com/2227-7390/9/5/539 |
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