A system of generalized Sylvester quaternion matrix equations and its applications

作者：Zhang, Xiang^*

来源：Applied Mathematics and Computation, 2016, 273: 74-81.

DOI：10.1016/j.amc.2015.09.074

• System of matrix equation
• Quaternion
• General solution
• eta-Hermitian
• Moore-Penrose inverse

Let H-mxn be the set of all m x n matrices over the real quaternion algebra. We call that A is an element of H-nxn is eta-Hermitian if A = -eta A*eta, eta is an element of (i, j, k), where i,j, k are the quaternion units. Denote A(eta)* = -eta A*eta. In this paper, we derive some necessary and sufficient conditions for the solvability to the system of generalized Sylvester real quaternion matrix equations A(i)X(i) + YiBi + C(i)ZD(i) = E-i, (i =1, 2), and give an expression of the general solution to the above mentioned system. As applications, we give some solvability conditions and general solution for the generalized Sylvester real quaternion matrix equation A(1)X + YB1 + C(1)ZD(1) = E-1, where Z is required to be eta-Hermitian. We also present some solvability conditions and general solution for the system of real quaternion matrix equations involving eta-Hermicity A(i)X(i) + (A(i)X(i))(eta)* + BiYBi eta* (i = 1, 2), where Y is required to be eta-Hermitian. Our results include some well-known results as special cases.

• 出版日期2016-1-15
• 单位贵州师范大学