论文标题
在矩阵集中，在结合下不变并采用通勤元素的线性组合
On matrix sets invariant under conjugation and taking linear combinations of commuting elements
论文作者
论文摘要
矩阵代数的子集在结合下不变并包含其两个通勤元素的线性跨度。它们显然包括可对角和尼尔氏矩阵的子集。在论文中，考虑了代数封闭场的情况。该问题很容易减少到具有给定特性的Nilpotent矩阵的对角矩阵和子集的子集的描述。因此，在可对角矩阵中，有四个这样的子集。至于Nilpotent情况，可以证明该子集应由矩阵的所有Jordan单元的大小属于某个数字集的条件来定义。根据本集获得了明确的标准。
Subsets of a matrix algebra over a field that are invariant under conjugation and contain the linear span of each two of their commuting elements are described. They obviously include the subsets of diagonalizable and nilpotent matrices. In the paper, the case of an algebraically closed field is considered. The problem is easily reduced to description of subsets of diagonalizable matrices and subsets of nilpotent matrices with the given properties. So, among diagonalizable matrices, there are four of such subsets. As for the nilpotent case, it is proved that the subset should be defined by the condition that the sizes of all Jordan cells of the matrix belong to a certain number set. An explicit criterion is obtained in terms of this set.
