论文标题
$ 4 \ times 4 $正骨变化
The $4 \times 4$ orthostochastic variety
论文作者
论文摘要
正静态矩阵是正交矩阵的进入方形，并且在各种情况下自然出现，包括实际多项式的明显确定的对称确定性表示。但是，实际品种的定义方程式以前仅以$ 3 \ times 3 $矩阵而闻名。我们研究了$ 4 \ times 4 $正骨矩阵的实际品种，并找到一组最少的定义方程组，该方程组成的方程组成，包括6个五分之一和3个八卦。此处使用的技术涉及计算机代数和数值代数几何形状的各种符号和计算方法。
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 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.
