论文标题
实际仿射子空间中的单数矢量
Singular Vectors in Real Affine Subspaces
论文作者
论文摘要
我们证明了这些仿射子空间内仿射子空间和子元的单数向量集的零属性的继承。我们为矩阵定义了$ n $ singularity的概念，这与非理性的统一指数密切相关。对于某些仿射子空间，我们表明，当且仅当参数化矩阵不是$ n $ singular时，单数向量集的测量为零。特别是，当且仅当参数化矩阵不合理时，我们显示了仿射超植物的单数矢量集的测量为零。
We prove inheritance of measure zero property of the set of singular vectors for affine subspaces and submanifolds inside those affine subspaces. We define a notion of $n$-singularity for matrices, which is closely related to the uniform exponent of irrationality. For certain affine subspaces, we show that the set of singular vectors has measure zero if and only if the parametrizing matrix is not $n$-singular. In particular, we show for affine hyperplanes the set of singular vectors has measure zero if and only if the parametrizing matrix is not rational.
