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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| Дата: | 2019 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2019
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-188430 |
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dspace |
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irk-123456789-1884302023-03-02T01:27:08Z A family of doubly stochastic matrices involving Chebyshev polynomials Ahmed, T. Caballero, J.M.R. 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). 2019 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/188430 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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). |
| format |
Article |
| author |
Ahmed, T. Caballero, J.M.R. |
| spellingShingle |
Ahmed, T. Caballero, J.M.R. A family of doubly stochastic matrices involving Chebyshev polynomials Algebra and Discrete Mathematics |
| author_facet |
Ahmed, T. Caballero, J.M.R. |
| author_sort |
Ahmed, T. |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2019 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188430 |
| 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. |
| series |
Algebra and Discrete Mathematics |
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2023-10-18T23:08:21Z |
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2023-10-18T23:08:21Z |
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