论文标题
带有分区特征值的真实对称矩阵
Real Symmetric Matrices with Partitioned Eigenvalues
论文作者
论文摘要
我们研究了由分区确定的特征值多样性的真实对称矩阵的真实代数种类。我们提出了维度和欧几里得距离度的公式。我们通过有理功能给出参数化。对于小矩阵，我们提供方程式；对于较大的矩阵，我们解释了如何使用表示理论查找方程。我们在正交群体的作用下描述了不变的环。对于对角线矩阵的子不同，我们给出了该学位。
We study the real algebraic variety of real symmetric matrices with eigenvalue multiplicities determined by a partition. We present formulas for the dimension and Euclidean distance degree. We give a parametrization by rational functions. For small matrices, we provide equations; for larger matrices, we explain how to use representation theory to find equations. We describe the ring of invariants under the action of the orthogonal group. For the subvariety of diagonal matrices, we give the degree.
