Kronecker Bases for Linear Matrix Equations, With Application to Two-Parameter Eigenvalue Problems
Kronecker Bases for Linear Matrix Equations, With Application to Two-Parameter Eigenvalue Problems
复制标题
线性矩阵方程的克罗内克基及其在二参数特征值问题中的应用
DOI：
10.1016/0024-3795(95)00361-4
复制
发表时间：
1996
影响因子：
1.1
通讯作者：
T. Kosir
中科院分区：
文献类型：
--
作者：
T. Kosir
齐次矩阵方程 AXCT− BXDT= 0 和矩阵方程组 AX + BY = 0, XCT+ YDT= 0 的通解用克罗内克规范形式描述，即，对于矩阵对 (A, B) 和 (C, D)，用克罗内克不变量和克罗内克基来描述。讨论了一对交换矩阵 (E, F) 的规范形式，使得 E2= F2= EF = 0。这些结果应用于构建双参数特征值问题的第二根子空间的规范基础。给出了规范不变量的对应关系。
The general solutions of the homogeneous matrix equation AXCT− BXDT= 0 and the system of the matrix equations AX + BY = 0, XCT+ YDT= 0 are described in terms of Kronecker canonical forms, i.e., in terms of Kronecker invariants and Kronecker bases, for pairs of matrices (A, B) and (C, D). A canonical form for a pair of commuting matrices (E, F) such that E2= F2= EF = 0 is discussed. These results are applied to construct a canonical basis for the second root subspace of a two-parameter eigenvalue problem. The corresponding relations for canonical invariants are given.