Norm of nonnegative and positive matrices

Alaa Abu Alroz

doi:10.14419/ijamr.v6i3.7637

Authors

Alaa Abu Alroz
Jordanian university

Received date: April 23, 2017

Accepted date: May 22, 2017

Published date: July 26, 2017

DOI:

https://doi.org/10.14419/ijamr.v6i3.7637

Keywords:

Nonnegative Matrix, Positive Matrix, Spectral Radius, Perron Roots of Nonnegative Matrix.

Abstract

The spectral radius r(A) of matrix A is the maximum modulus of the Eigen values. In this paper, the studies about the lower and upper bounds for the spectral radius and the lower bounds for the minimum eigen value of appositive and nonnegative matrices are investigate.
The matrix norm, the spectral radius norm,and the column (row) sums of nonnegative and positive matrices are widely used to establish some inequalities for matrices. Then several existing results are improved for these inequalities for nonnegative and positive matrix. Furthermore, the lower and upper bounds of the Perron roots for nonnegative matrices are examined, and some upper bounds are computed.

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