https://orcid.org/0000-0002-2387-7169
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ABSTRACT
Orthostochastic matrices are the entrywise squares of orthogonal matrices, and naturally arise in various contexts, including notably definite symmetric determinantal representations of real polynomials. However, defining equations for the real variety were previously known only for 3 × 3 matrices. We study the real variety of 4 × 4 orthostochastic matrices, and find a minimal defining set of equations consisting of 6 quintics and 3 octics. The techniques used here involve a wide range of both symbolic and computational methods, in computer algebra and numerical algebraic geometry.
Correction Statement
This article has been republished with minor changes. These changes do not impact the academic content of the article.
Acknowledgments
Both authors are grateful to ICERM for enabling collaboration which led to this project. The second author thanks to Paul Breiding, Mateusz Michalek and Bernd Sturmfels for their encouragement toward work on this project.
Declaration of Interest
No potential conflict of interest was reported by the author(s).