Eventually DSDD Matrices and Eigenvalue Localization

Firstly, the relationships among strictly diagonally dominant ( S D D ) matrices, doubly strictly diagonally dominant ( D S D D ) matrices, eventually S D D matrices and eventually D S D D matrices are considered. Secondly, by excluding some proper subsets of an existing...

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Main Authors:	Caili Sang, Jianxing Zhao
Format:	Article
Language:	English
Published:	MDPI AG 2018-10-01
Series:	Symmetry
Subjects:	matrices strictly diagonally dominant eigenvalue localization determinant infinity norm
Online Access:	http://www.mdpi.com/2073-8994/10/10/448

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spelling	doaj-1eb61b0d608b4ebab9c029f6badf4fec2020-11-24T21:48:37ZengMDPI AGSymmetry2073-89942018-10-01101044810.3390/sym10100448sym10100448Eventually DSDD Matrices and Eigenvalue LocalizationCaili Sang0Jianxing Zhao1College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, Guizhou, ChinaCollege of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, Guizhou, ChinaFirstly, the relationships among strictly diagonally dominant ( S D D ) matrices, doubly strictly diagonally dominant ( D S D D ) matrices, eventually S D D matrices and eventually D S D D matrices are considered. Secondly, by excluding some proper subsets of an existing eigenvalue inclusion set for matrices, which do not contain any eigenvalues of matrices, a tighter eigenvalue inclusion set of matrices is derived. As its application, a sufficient condition of determining non-singularity of matrices is obtained. Finally, the infinity norm estimation of the inverse of eventually D S D D matrices is derived.http://www.mdpi.com/2073-8994/10/10/448matricesstrictly diagonally dominanteigenvalue localizationdeterminantinfinity norm
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Caili Sang Jianxing Zhao
spellingShingle	Caili Sang Jianxing Zhao Eventually DSDD Matrices and Eigenvalue Localization Symmetry matrices strictly diagonally dominant eigenvalue localization determinant infinity norm
author_facet	Caili Sang Jianxing Zhao
author_sort	Caili Sang
title	Eventually DSDD Matrices and Eigenvalue Localization
title_short	Eventually DSDD Matrices and Eigenvalue Localization
title_full	Eventually DSDD Matrices and Eigenvalue Localization
title_fullStr	Eventually DSDD Matrices and Eigenvalue Localization
title_full_unstemmed	Eventually DSDD Matrices and Eigenvalue Localization
title_sort	eventually dsdd matrices and eigenvalue localization
publisher	MDPI AG
series	Symmetry
issn	2073-8994
publishDate	2018-10-01
description	Firstly, the relationships among strictly diagonally dominant ( S D D ) matrices, doubly strictly diagonally dominant ( D S D D ) matrices, eventually S D D matrices and eventually D S D D matrices are considered. Secondly, by excluding some proper subsets of an existing eigenvalue inclusion set for matrices, which do not contain any eigenvalues of matrices, a tighter eigenvalue inclusion set of matrices is derived. As its application, a sufficient condition of determining non-singularity of matrices is obtained. Finally, the infinity norm estimation of the inverse of eventually D S D D matrices is derived.
topic	matrices strictly diagonally dominant eigenvalue localization determinant infinity norm
url	http://www.mdpi.com/2073-8994/10/10/448
work_keys_str_mv	AT cailisang eventuallydsddmatricesandeigenvaluelocalization AT jianxingzhao eventuallydsddmatricesandeigenvaluelocalization
_version_	1725891217851416576

Eventually DSDD Matrices and Eigenvalue Localization

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