The group of monomial matrices

Authors

  • Martin F. Martinez University of Washington Bothell
  • Pietro Paparella University of Washington Bothell

DOI:

https://doi.org/10.33043/94EV9NDNHD

Abstract

A recent result is used to give a brief proof of the well-known fact that the set of monomial matrices forms a subgroup of the set of invertible matrices. In addition, another proof is given of the result that the inverse of an invertible nonnegative matrix is nonnegative if and only if the matrix is monomial.

Author Biographies

Martin F. Martinez, University of Washington Bothell

Martin Martinez worked on this paper as a dual-enrolled high school student. He is now majoring in mathematics at the University of Washington Bothell. In his spare time, he enjoys learning about and working with electronic music production.

Pietro Paparella, University of Washington Bothell

Pietro Paparella received the Ph.D. degree in mathematics from Washington State University in 2013 and is currently an Associate Professor of mathematics in the Division of Engineering and Mathematics at the University of Washington Bothell. His research interests are in nonnegative matrix theory, combinatorial matrix theory, discrete geometry, and the geometry of polynomials. His hobbies include guitar playing, charcoal drawing, and oil painting.

References

J. Ding and N. H. Rhee. Teaching tip: when a matrix and its inverse are stochastic. College Math. J., 44(2):108–109, 2013.

J. Ding and N. H. Rhee. When a matrix and its inverse are nonnegative. Missouri J. Math. Sci., 26(1):98–103, 2014.

C. R. Johnson and P. Paparella. Perron spectratopes and the real nonnegative inverse eigenvalue problem. Linear Algebra Appl., 493:281–300, 2016.

C. R. Johnson and H. M. Shapiro. Mathematical aspects of the relative gain array (A◦A^(−T)). SIAM J. Algebraic Discrete Methods, 7(4):627–644, 1986.

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Published

2026-03-03

How to Cite

Martinez, M., & Paparella, P. (2026). The group of monomial matrices. Mathematics Exchange, 17(1), 34–38. https://doi.org/10.33043/94EV9NDNHD

Issue

Vol. 17 No. 1 (2023): Mathematics Exchange, Fall 2023

Section

Articles

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Copyright (c) 2026 Martin F. Martinez, Pietro Paparella

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.