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Open AccessArticle

Eventually DSDD Matrices and Eigenvalue Localization

by 1,2 and 1,*
1
College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, Guizhou, China
2
School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, Guizhou, China
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(10), 448; https://doi.org/10.3390/sym10100448
Received: 6 September 2018 / Revised: 22 September 2018 / Accepted: 26 September 2018 / Published: 1 October 2018
(This article belongs to the Special Issue Symmetry in Numerical Linear and Multilinear Algebra)
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. View Full-Text
Keywords: matrices; strictly diagonally dominant; eigenvalue localization; determinant; infinity norm matrices; strictly diagonally dominant; eigenvalue localization; determinant; infinity norm
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Sang, C.; Zhao, J. Eventually DSDD Matrices and Eigenvalue Localization. Symmetry 2018, 10, 448.

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