Polynomials that Preserve Nonnegative Matrices of Order Two

Benjamin Clark; Pietro Paparella

doi:10.33043/AM5MAEyBVA

Authors

Benjamin J. Clark University of Washington Bothell
Pietro Paparella University of Washington Bothell

DOI:

https://doi.org/10.33043/AM5MAEyBVA

Abstract

A known characterization for entire functions that preserve all nonnegative matrices of order two is shown to characterize polynomials that preserve nonnegative matrices of order two. Equivalent conditions are derived and used to prove that P3 ⊂ P2, which was previously unknown. A new characterization is given for polynomials that preserve nonnegative circulant matrices of order two.

Author Biographies

Benjamin J. Clark, University of Washington Bothell

A known characterization for entire functions that preserve all nonnegative matrices of order two is shown to characterize polynomials that preserve nonnegative matrices of order two. Equivalent conditions are derived and used to prove that P3 ⊂ P2, which was previously unknown. A new characterization is given for polynomials that preserve nonnegative circulant matrices of order two.

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

G. Bharali and O. Holtz. Functions preserving nonnegativity of matrices. SIAM J. Matrix Anal. Appl., 30(1):84–101, 2008.

B. J. Clark and P. Paparella. Polynomials that preserve nonnegative matrices. Linear Algebra Appl., 637:110–118, 2022.

R. Loewy and D. London. A note on an inverse problem for nonnegative matrices. Linear and Multilinear Algebra, 6(1):83–90, 1978/79.

P. Paparella. Matrix functions that preserve the strong Perron-Frobenius property. Electron. J. Linear Algebra, 30:271–278, 2015.

V. Powers and B. Reznick. Polynomials that are positive on an interval. Trans. Amer. Math. Soc., 352(10):4677–4692, 2000.

Polynomials that Preserve Nonnegative Matrices of Order Two

Authors

DOI:

Abstract

Author Biographies

Benjamin J. Clark, University of Washington Bothell

Pietro Paparella, University of Washington Bothell

References

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