When a Matrix and Its Inverse Are Nonnegative

Authors

Jiu Ding, University of Southern MississippiFollow
N. H. Rhee, University of Missouri-Kansas CityFollow

Document Type

Article

Publication Date

5-1-2014

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

In this article we prove that A and A⁻¹ are stochastic if and only if A is a permutation matrix. Then we extend this result to show that A and A⁻¹ are nonnegative if and only if it is a product of a diagonal matrix with all positive diagonal entries and a permutation matrix.

Publication Title

Missouri Journal of Mathematical Sciences

Volume

26

Issue

1

First Page

98

Last Page

103

Recommended Citation

Ding, J., Rhee, N. (2014). When a Matrix and Its Inverse Are Nonnegative. Missouri Journal of Mathematical Sciences, 26(1), 98-103.
Available at: https://aquila.usm.edu/fac_pubs/19923