文献类型：期刊文献

英文题名：Ranks of a Constrained Hermitian Matrix Expression with Applications

作者：Yu, Shao-Wen

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2013

外文期刊名：JOURNAL OF APPLIED MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000315906800001)】；

基金：This research was supported by the National Natural Science Foundation of China, Tian Yuan Foundation (11226067), the Fundamental Research Funds for the Central Universities (WM1214063), and China Postdoctoral Science Foundation (2012M511014).

语种：英文

摘要：We establish the formulas of the maximal and minimal ranks of the quaternion Hermitian matrix expression C-4 - A(4)XA(4)* where X is a Hermitian solution to quaternion matrix equations A(1)X = C-1, XB1 = C-2, and A(3)XA(3)* = C-3. As applications, we give a new necessary and sufficient condition for the existence of Hermitian solution to the system of matrix equations A(1)X = C-1, XB1 = C-2, A(3)XA(3)* = C-3, and A(4)XA(4)* = C-4, which was investigated by Wang and Wu, 2010, by rank equalities. In addition, extremal ranks of the generalized Hermitian Schur complement C-4 - A(4)A(3)(similar to)A(4)* with respect to a Hermitian g-inverse A(3)(similar to) of A(3), which is a common solution to quaternion matrix equations A(1)X = C-1 and XB1 = C-2, are also considered.