A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers

We use a new method of matrix decomposition for r-circulant matrix to get the determinants of An=CircrF1,F2,…,Fn and Bn=CircrL1,L2,…,Ln, where Fn is the Fibonacci numbers and Ln is the Lucas numbers. Based on these determinants and the nonsingular conditions, inverse matrices are derived. The expres...

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Autores principales:	Jiangming Ma, Tao Qiu, Chengyuan He
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/81d056a53b2744cabcbd3cc20ee534de
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spelling	oai:doaj.org-article:81d056a53b2744cabcbd3cc20ee534de2021-11-29T00:56:33ZA New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers2314-478510.1155/2021/4782594https://doaj.org/article/81d056a53b2744cabcbd3cc20ee534de2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/4782594https://doaj.org/toc/2314-4785We use a new method of matrix decomposition for r-circulant matrix to get the determinants of An=CircrF1,F2,…,Fn and Bn=CircrL1,L2,…,Ln, where Fn is the Fibonacci numbers and Ln is the Lucas numbers. Based on these determinants and the nonsingular conditions, inverse matrices are derived. The expressions of the determinants and inverse matrices are represented by Fibonacci and Lucas Numbers. In this study, the formulas of determinants and inverse matrices are much simpler and concise for programming and reduce the computational time.Jiangming MaTao QiuChengyuan HeHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Jiangming Ma Tao Qiu Chengyuan He A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers
description	We use a new method of matrix decomposition for r-circulant matrix to get the determinants of An=CircrF1,F2,…,Fn and Bn=CircrL1,L2,…,Ln, where Fn is the Fibonacci numbers and Ln is the Lucas numbers. Based on these determinants and the nonsingular conditions, inverse matrices are derived. The expressions of the determinants and inverse matrices are represented by Fibonacci and Lucas Numbers. In this study, the formulas of determinants and inverse matrices are much simpler and concise for programming and reduce the computational time.
format	article
author	Jiangming Ma Tao Qiu Chengyuan He
author_facet	Jiangming Ma Tao Qiu Chengyuan He
author_sort	Jiangming Ma
title	A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers
title_short	A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers
title_full	A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers
title_fullStr	A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers
title_full_unstemmed	A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers
title_sort	new method of matrix decomposition to get the determinants and inverses of r-circulant matrices with fibonacci and lucas numbers
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/81d056a53b2744cabcbd3cc20ee534de
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A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers

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