论文标题
给定子空间中的特征向量的张量
Tensors with eigenvectors in a given subspace
论文作者
论文摘要
B. sturmfels的第一作者研究了给定线性子空间中的特征向量的各种矩阵，称为Kalman Variety。我们将这项研究从矩阵扩展到对称张量，证明了张量设定了卡尔曼品种的不可还原性并计算其编成矩阵和程度。此外，我们考虑具有给定线性子空间中第一个组件的单数T型的Kalman种类量，我们证明了类似的结果，即使在矩阵的情况下，它们也是新的。主要技术来自代数的几何形状，使用Chern类进行列举计算。
The first author with B. Sturmfels studied the variety of matrices with eigenvectors in a given linear subspace, called Kalman variety. We extend that study from matrices to symmetric tensors, proving in the tensor setting the irreducibility of the Kalman variety and computing its codimension and degree. Furthermore we consider the Kalman variety of tensors having singular t-ples with the first component in a given linear subspace and we prove analogous results, which are new even in the case of matrices. Main techniques come from Algebraic Geometry, using Chern classes for enumerative computations.
