Open Access
May 2014 When a Matrix and Its Inverse Are Nonnegative
J. Ding, N. H. Rhee
Missouri J. Math. Sci. 26(1): 98-103 (May 2014). DOI: 10.35834/mjms/1404997113


In this article we prove that $A$ and $A^{-1}$ are stochastic if and only of $A$ 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.


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J. Ding. N. H. Rhee. "When a Matrix and Its Inverse Are Nonnegative." Missouri J. Math. Sci. 26 (1) 98 - 103, May 2014.


Published: May 2014
First available in Project Euclid: 10 July 2014

zbMATH: 1339.15022
MathSciNet: MR3263545
Digital Object Identifier: 10.35834/mjms/1404997113

Primary: 15A18‎

Keywords: Nonnegative matrix , permutation matrix , stochastic matrix

Rights: Copyright © 2014 Central Missouri State University, Department of Mathematics and Computer Science

Vol.26 • No. 1 • May 2014
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