NEW BOUNDS FOR THE MAXIMAL EIGENVALUES
OF POSITIVE DEFINITE MATRICES
P. Singh1, V. Singh1, S. Singh2
1University of KwaZulu-Natal
Private Bag X54001
Durban - 4001, SOUTH AFRICA
2University of South Africa
Department of Decision Sciences
P.O. Box 392, Pretoria - 0003, SOUTH AFRICA

Abstract

In this paper, we improve earlier bounds on the extremal eigenvalues of positive definite matrices by introducing an increasing function and by considering a vector function of the eigenvalues. For various choices of the monotonic function we are able to obtain bounds for the extremal eigenvalues in terms of the traces of the matrix and its powers. Our bounds are a function of two parameters achieved by using Jensen's inequality. These bounds are relatively simple to compute.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 5
Year: 2022

DOI: 10.12732/ijam.v35i5.4

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