In this paper, the maximal and minimal ranks of the solution to a system of matrix equations over H, the real quaternion algebra, were derived. A previous known result could be regarded as a special case of the new re...In this paper, the maximal and minimal ranks of the solution to a system of matrix equations over H, the real quaternion algebra, were derived. A previous known result could be regarded as a special case of the new result.展开更多
A new expression is established for the common solution to six classical linear quaternion matrix equations A 1 X = C 1 , X B 1 = C 3 , A 2 X = C 2 , X B 2 = C 4 , A 3 X B 3 = C 5 , A 4 X B 4 = C 6 which was investiga...A new expression is established for the common solution to six classical linear quaternion matrix equations A 1 X = C 1 , X B 1 = C 3 , A 2 X = C 2 , X B 2 = C 4 , A 3 X B 3 = C 5 , A 4 X B 4 = C 6 which was investigated recently by Wang, Chang and Ning （Q. Wang, H. Chang, Q. Ning, The common solution to six quaternion matrix equations with applications, Appl. Math. Comput. 195： 721-732 （2008））. Formulas are derived for the maximal and minimal ranks of the common solution to this system. Moreover, corresponding results on some special cases are presented. As an application, a necessary and sufficient condition is presented for the invariance of the rank of the general solution to this system. Some known results can be regarded as the special cases of the results in this paper.展开更多
In this paper, we give the expression of the least square solution of the linear quaternion matrix equation AXB = C subject to a consistent system of quaternion matrix equations D1X = F1, XE2 =F2, and derive the maxim...In this paper, we give the expression of the least square solution of the linear quaternion matrix equation AXB = C subject to a consistent system of quaternion matrix equations D1X = F1, XE2 =F2, and derive the maximal and minimal ranks and the leastnorm of the above mentioned solution. The finding of this paper extends some known results in the literature.展开更多
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 ...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.展开更多
In this paper we investigate the system of linear matrix equations A1X = C1, YB2 = C2, A3XB3 = C3, A4YB4 = C4, BX ＋ YC = A. We present some necessary and sufficient conditions for the existence of a solution to this ...In this paper we investigate the system of linear matrix equations A1X = C1, YB2 = C2, A3XB3 = C3, A4YB4 = C4, BX ＋ YC = A. We present some necessary and sufficient conditions for the existence of a solution to this system and give an expression of the general solution to the system when the solvability conditions are satisfied.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No.60672160）
文摘In this paper, the maximal and minimal ranks of the solution to a system of matrix equations over H, the real quaternion algebra, were derived. A previous known result could be regarded as a special case of the new result.
基金Supported by the National Natural Science Foundation of Shanghai (No. 11ZR1412500)the Ph.D. Programs Foundation of Ministry of Education of China (No. 20093108110001)Shanghai Leading Academic Discipline Project (No. J50101)
文摘A new expression is established for the common solution to six classical linear quaternion matrix equations A 1 X = C 1 , X B 1 = C 3 , A 2 X = C 2 , X B 2 = C 4 , A 3 X B 3 = C 5 , A 4 X B 4 = C 6 which was investigated recently by Wang, Chang and Ning （Q. Wang, H. Chang, Q. Ning, The common solution to six quaternion matrix equations with applications, Appl. Math. Comput. 195： 721-732 （2008））. Formulas are derived for the maximal and minimal ranks of the common solution to this system. Moreover, corresponding results on some special cases are presented. As an application, a necessary and sufficient condition is presented for the invariance of the rank of the general solution to this system. Some known results can be regarded as the special cases of the results in this paper.
文摘In this paper, we give the expression of the least square solution of the linear quaternion matrix equation AXB = C subject to a consistent system of quaternion matrix equations D1X = F1, XE2 =F2, and derive the maximal and minimal ranks and the leastnorm of the above mentioned solution. The finding of this paper extends some known results in the literature.
文摘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.
基金This research was supported by the grants from the National Natural Science Foundation of China （11571220, 11171205）.
文摘In this paper we investigate the system of linear matrix equations A1X = C1, YB2 = C2, A3XB3 = C3, A4YB4 = C4, BX ＋ YC = A. We present some necessary and sufficient conditions for the existence of a solution to this system and give an expression of the general solution to the system when the solvability conditions are satisfied.
