A family of doubly stochastic matrices involving Chebyshev polynomials
A doubly stochastic matrix is a square matrix \(A=(a_{ij})\) of non-negative real numbers such that \(\sum_{i}a_{ij}=\sum_{j}a_{ij}=1\). The Chebyshev polynomial of the first kind is defined by the recurrence relation \(T_0(x)=1, T_1(x)=x\), and \[T_{n+1}(x)=2xT_n(x)-T_{n-1}(x).\]In this paper, we s...
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| Datum: | 2019 |
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Lugansk National Taras Shevchenko University
2019
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oai:ojs.admjournal.luguniv.edu.ua:article-5572019-07-14T19:54:06Z A family of doubly stochastic matrices involving Chebyshev polynomials Ahmed, Tanbir Caballero, José Manuel Rodriguez doubly stochastic matrices, Chebyshev polynomials A doubly stochastic matrix is a square matrix \(A=(a_{ij})\) of non-negative real numbers such that \(\sum_{i}a_{ij}=\sum_{j}a_{ij}=1\). The Chebyshev polynomial of the first kind is defined by the recurrence relation \(T_0(x)=1, T_1(x)=x\), and \[T_{n+1}(x)=2xT_n(x)-T_{n-1}(x).\]In this paper, we show a \(2^k\times 2^k\) (for each integer \(k\geq 1\)) doubly stochastic matrix whose characteristic polynomial is \(x^2-1\) times a product of irreducible Chebyshev polynomials of the first kind (up to rescaling by rational numbers). Lugansk National Taras Shevchenko University 2019-07-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/557 Algebra and Discrete Mathematics; Vol 27, No 2 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/557/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/557/540 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/557/541 Copyright (c) 2019 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
doubly stochastic matrices Chebyshev polynomials |
| spellingShingle |
doubly stochastic matrices Chebyshev polynomials Ahmed, Tanbir Caballero, José Manuel Rodriguez A family of doubly stochastic matrices involving Chebyshev polynomials |
| topic_facet |
doubly stochastic matrices Chebyshev polynomials |
| format |
Article |
| author |
Ahmed, Tanbir Caballero, José Manuel Rodriguez |
| author_facet |
Ahmed, Tanbir Caballero, José Manuel Rodriguez |
| author_sort |
Ahmed, Tanbir |
| title |
A family of doubly stochastic matrices involving Chebyshev polynomials |
| title_short |
A family of doubly stochastic matrices involving Chebyshev polynomials |
| title_full |
A family of doubly stochastic matrices involving Chebyshev polynomials |
| title_fullStr |
A family of doubly stochastic matrices involving Chebyshev polynomials |
| title_full_unstemmed |
A family of doubly stochastic matrices involving Chebyshev polynomials |
| title_sort |
family of doubly stochastic matrices involving chebyshev polynomials |
| description |
A doubly stochastic matrix is a square matrix \(A=(a_{ij})\) of non-negative real numbers such that \(\sum_{i}a_{ij}=\sum_{j}a_{ij}=1\). The Chebyshev polynomial of the first kind is defined by the recurrence relation \(T_0(x)=1, T_1(x)=x\), and \[T_{n+1}(x)=2xT_n(x)-T_{n-1}(x).\]In this paper, we show a \(2^k\times 2^k\) (for each integer \(k\geq 1\)) doubly stochastic matrix whose characteristic polynomial is \(x^2-1\) times a product of irreducible Chebyshev polynomials of the first kind (up to rescaling by rational numbers). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2019 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/557 |
| work_keys_str_mv |
AT ahmedtanbir afamilyofdoublystochasticmatricesinvolvingchebyshevpolynomials AT caballerojosemanuelrodriguez afamilyofdoublystochasticmatricesinvolvingchebyshevpolynomials AT ahmedtanbir familyofdoublystochasticmatricesinvolvingchebyshevpolynomials AT caballerojosemanuelrodriguez familyofdoublystochasticmatricesinvolvingchebyshevpolynomials |
| first_indexed |
2024-04-12T06:25:19Z |
| last_indexed |
2024-04-12T06:25:19Z |
| _version_ |
1796109220359176192 |