A family of doubly stochastic matrices involving Chebyshev polynomials
A doubly stochastic matrix is a square matrix A = (aij) of non-negative real numbers such that ∑i aij =∑j aij =1. The Chebyshev polynomial of the first kind is defined by the recurrence relation T₀ (x) = 1, T₁ (x) = x, and Tn+1(x) = 2xTn(x) − Tn−1(x). In this paper, we show a 2ᵏ ×2ᵏ (for each intege...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2019 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/188430 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A family of doubly stochastic matrices involving Chebyshev polynomials / T. Ahmed, J.M.R. Caballero // Algebra and Discrete Mathematics. — 2019. — Vol. 27, № 2. — С. 155–164. — Бібліогр.: 2 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862589739285086208 |
|---|---|
| author | Ahmed, T. Caballero, J.M.R. |
| author_facet | Ahmed, T. Caballero, J.M.R. |
| citation_txt | A family of doubly stochastic matrices involving Chebyshev polynomials / T. Ahmed, J.M.R. Caballero // Algebra and Discrete Mathematics. — 2019. — Vol. 27, № 2. — С. 155–164. — Бібліогр.: 2 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | A doubly stochastic matrix is a square matrix A = (aij) of non-negative real numbers such that ∑i aij =∑j aij =1. The Chebyshev polynomial of the first kind is defined by the recurrence relation T₀ (x) = 1, T₁ (x) = x, and Tn+1(x) = 2xTn(x) − Tn−1(x). In this paper, we show a 2ᵏ ×2ᵏ (for each integer k > 1) doubly stochastic matrix whose characteristic polynomial is x² − 1 times a product of irreducible Chebyshev polynomials of the first kind (upto rescaling by rational numbers).
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| first_indexed | 2025-11-27T03:40:09Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188430 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-27T03:40:09Z |
| publishDate | 2019 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Ahmed, T. Caballero, J.M.R. 2023-03-01T15:26:38Z 2023-03-01T15:26:38Z 2019 A family of doubly stochastic matrices involving Chebyshev polynomials / T. Ahmed, J.M.R. Caballero // Algebra and Discrete Mathematics. — 2019. — Vol. 27, № 2. — С. 155–164. — Бібліогр.: 2 назв. — англ. 1726-3255 2010 MSC: Primary 05D10. https://nasplib.isofts.kiev.ua/handle/123456789/188430 A doubly stochastic matrix is a square matrix A = (aij) of non-negative real numbers such that ∑i aij =∑j aij =1. The Chebyshev polynomial of the first kind is defined by the recurrence relation T₀ (x) = 1, T₁ (x) = x, and Tn+1(x) = 2xTn(x) − Tn−1(x). In this paper, we show a 2ᵏ ×2ᵏ (for each integer k > 1) doubly stochastic matrix whose characteristic polynomial is x² − 1 times a product of irreducible Chebyshev polynomials of the first kind (upto rescaling by rational numbers). en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics A family of doubly stochastic matrices involving Chebyshev polynomials Article published earlier |
| spellingShingle | A family of doubly stochastic matrices involving Chebyshev polynomials Ahmed, T. Caballero, J.M.R. |
| title | 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_short | A family of doubly stochastic matrices involving Chebyshev polynomials |
| title_sort | family of doubly stochastic matrices involving chebyshev polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188430 |
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