Ranks of Submatrices in a Solution to a Consistent System of Linear Quaternion Matrix Equations with Applications

• 作者: Chunyan Lin
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 四元数矩阵方程 子矩阵 系统 应用 线性 广义逆 溶液
• 年，卷（期）: 2014,（3）
• 页码范围: 399-410
• 页数: 12页
• 分类号: O151.21
• 语种: 中文

摘要

Suppose that A1X = C1, XB2 = C2, A3XB3= 63 is a consistent system of matrix equations and partition its solution X into a 2* 2 block form. In this paper, we give formulas for the maximal and minimal ranks of the submatrices in a solution X to the system. We also investigate the uniqueness and the independence of submatrices in a solution X. As applications, we give some properties of submatrices in generalized inverses of matrices. These extend some known results in the literature.