The Gerschgorin Disk Theorem and Regularity Conditions for Complex Interval Matrices

doi:10.3969/j.issn.1006-8074.2024.01.008

Mathematical Theory and Applications ›› 2024, Vol. 44 ›› Issue (1): 109-121.doi: 10.3969/j.issn.1006-8074.2024.01.008

The Gerschgorin Disk Theorem and Regularity Conditions for Complex Interval Matrices

Cheng Long¹, Xia Dandan¹,Li Yaotang^2,*

1. School of Mathematics and Computer Science, Chongqing University of International Business and Economics, Chongqing 401520, China; 2. School of Mathematics and Statistics, Yunnan University, Kunming 650091, China

Online:2024-03-28 Published:2024-04-16

Abstract

Abstract: In this paper, the Gerschgorin disk theorem on eigenvalues of complex matrices is generalized to complex interval matrices, in which the Gerschgorin disk regions of eigenvalues of complex interval matrices are presented. It is showed that the Gerschgorin disk regions are contained in the Gerschgorin square regions for eigenvalues of complex interval matrices. Then, two new sufficient conditions for the regularity of complex interval matrices are obtained by applying the Gerschgorin disk theorem of complex interval matrices.

Key words: Complex interval matrix, Eigenvalue, Gerschgorin disk theorem, Regularity

Cheng Long, Xia Dandan, Li Yaotang. The Gerschgorin Disk Theorem and Regularity Conditions for Complex Interval Matrices[J]. Mathematical Theory and Applications, 2024, 44(1): 109-121.

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The Gerschgorin Disk Theorem and Regularity Conditions for Complex Interval Matrices

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