IJAM: Volume 38, No. 1 (2025)

DOI: 10.12732/ijam.v38i1.5

PROJECTIVE EIGENVALUE BOUNDS

P. Singh 1 , S. Singh 2, V. Singh 3

1 University of KwaZulu-Natal

Private Bag X54001, Durban, 4001

SOUTH AFRICA

2 University of South Africa

Department of Decision Sciences

PO Box 392 Pretoria, 0003

SOUTH AFRICA

3 University of KwaZulu-Natal

Private Bag X54001, Durban, 4001

SOUTH AFRICA

Abstract. In this paper, we derive expressions for the bounds of the eigenvalues of real symmetric matrices. We use symmetric projection operators

and also consider situations when some of the eigenvalues may be known. These bounds are based on the trace of the matrix and its Frobenius norm.

They are relatively easy and inexpensive to compute.

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How to cite this paper?
DOI: 10.12732/ijam.v38i1.5
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2025
Volume: 38
Issue: 1

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[10] P. Singh, S. Singh, V. Singh, Results on bounds of the spectrum of positive definite matrices by projections, Aust. J. Math. Anal. Appl.
20, No 2 (2023), Art. 3, 10 pp.

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