Paper Title:

Bounds for the Extremal Eigenvalues of Positive Definite Matrices

Author(s):

Shivani Singh and Pravin Singh

Unisa, Department of Decision Sciences,
PO Box 392,
Pretoria,
0003,
South Africa.
E-mail: singhs2@unisa.ac.za

University of KwaZulu-Natal,
School of Mathematics Statistics and Computer Sciences
Private Bag X54001,
Durban,
4000,
South Africa.
E-mail: singhprook@gmail.com

Abstract:

We use a projection to achieve bounds for a vector function of the eigenvalues of a positive definite matrix. 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. These bounds are relatively simple to compute.

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