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Paper Title:
Eigenvalue Bounds based on Projections
Author(s):
Pravin Singh, Shivani Singh, Virath Singh
University of KwaZulu-Natal,
Private Bag X54001,
Durban, 4001,
South Africa.
University of South Africa,
Department of Decision Sciences, PO Box 392,
Pretoria,0003,
South Africa.
University of KwaZulu-Natal,
Private Bag X54001,
Durban, 4001,
South Africa.
E-mail:
singhp@ukzn.ac.za,
singhs2@unisa.ac.za,
singhv@ukzn.ac.za
Abstract:
In this paper, we derive expressions for the bounds of the extremal eigenvalues of positive definite matrices. Our approach is to use a symmetric projection operator onto an n-2 dimensional subspace of the real space of n tuples. These bounds are based on traces of the matrix and its powers. They are relatively easy and inexpensive to compute.
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