The $4 \times 4$ orthostochastic variety
The $4 \times 4$ orthostochastic variety
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 $3 \times 3$ matrices. We study the real variety of $4 \times 4$ orthostochastic …