Distribution of Eigenvalues and Upper Bounds of the Spread of Interval Matrices

Wenshi Liao and Pujun Long ()
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Wenshi Liao: College of Mathematics, Physics and Data Science, Chongqing University of Science and Technology, Chongqing 401331, China
Pujun Long: College of Mathematics, Physics and Data Science, Chongqing University of Science and Technology, Chongqing 401331, China

Mathematics, 2023, vol. 11, issue 19, 1-10

Abstract: The distribution of eigenvalues and the upper bounds for the spread of interval matrices are significant in various fields of mathematics and applied sciences, including linear algebra, numerical analysis, control theory, and combinatorial optimization. We present the distribution of eigenvalues within interval matrices and determine upper bounds for their spread using Geršgorin’s theorem. Specifically, through an equality for the variance of a discrete random variable, we derive upper bounds for the spread of symmetric interval matrices. Finally, we give three numerical examples to illustrate the effectiveness of our results.

Keywords: interval matrices; distribution; eigenvalues; spread; upper bound (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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