论文标题
基质组中不可还原的控制属性
The irreducible control property in matrix groups
论文作者
论文摘要
本文涉及基质分解，其中这些因素仅限于矩阵组的封闭子变量。这样的分解与控制理论相关：鉴于该组中的靶矩阵，可以将其分解为次要数中元素的产物，以给定的顺序？如果是这样，关于解决此问题的解决方案可以说什么？是否可以将目标矩阵的不可还原曲线提升为不可约的分解曲线？我们表明，在某些条件下，对于足够长且复杂的序列，溶液集始终是不可还原的，并且我们表明，每个连接的矩阵组都有一个满足这些条件的单参数亚组的序列，其中该序列的长度小于该组维度的1.5倍。
This paper concerns matrix decompositions in which the factors are restricted to lie in a closed subvariety of a matrix group. Such decompositions are of relevance in control theory: given a target matrix in the group, can it be decomposed as a product of elements in the subvarieties, in a given order? And if so, what can be said about the solution set to this problem? Can an irreducible curve of target matrices be lifted to an irreducible curve of factorisations? We show that under certain conditions, for a sufficiently long and complicated such sequence, the solution set is always irreducible, and we show that every connected matrix group has a sequence of one-parameter subgroups that satisfies these conditions, where the sequence has length less than 1.5 times the dimension of the group.
