This paper first studies the solution of a complex matrix equation X - AXB = C, obtains an explicit solution of the equation by means of characteristic polynomial, and then studies the quaternion matrix equation X - A...This paper first studies the solution of a complex matrix equation X - AXB = C, obtains an explicit solution of the equation by means of characteristic polynomial, and then studies the quaternion matrix equation X - A X B = C, characterizes the existence of a solution to the matrix equation, and derives closed-form solutions of the matrix equation in explicit forms by means of real representations of quaternion matrices. This paper also gives an application to the complex matrix equation X - AXB =C.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
This paper studies a system of three Sylvester-type quaternion matrix equations with ten variables A_(i)X_(i)+Y_iB_(i)+C_(i)Z_(i)D_(i)+F_(i)Z_(i+1)G_(i)=E_(i),i=1,3^-.We derive some necessary and sufficient conditions...This paper studies a system of three Sylvester-type quaternion matrix equations with ten variables A_(i)X_(i)+Y_iB_(i)+C_(i)Z_(i)D_(i)+F_(i)Z_(i+1)G_(i)=E_(i),i=1,3^-.We derive some necessary and sufficient conditions for the existence of a solution to this system in terms of ranks and Moore–Penrose inverses of the matrices involved.We present the general solution to the system when the solvability conditions are satisfied.As applications of this system,we provide some solvability conditions and general solutions to some systems of quaternion matrix equations involvingφ-Hermicity.Moreover,we give some numerical examples to illustrate our results.The findings of this paper extend some known results in the literature.展开更多
This paper derives a theorem of generalized singular value decomposition of quaternion matrices （QGSVD）,studies the solution of general quaternion matrix equation AXB -CYD= E,and obtains quaternionic Roth＇s theorem...This paper derives a theorem of generalized singular value decomposition of quaternion matrices （QGSVD）,studies the solution of general quaternion matrix equation AXB -CYD= E,and obtains quaternionic Roth＇s theorem. This paper also suggests sufficient and necessary conditions for the existence and uniqueness of solutions and explicit forms of the solutions of the equation.展开更多
基金Supported by the National Natural Science Foundation of China (10371044)Shanghai Priority Academic Discipline Foundation, Shanghai, China
文摘This paper first studies the solution of a complex matrix equation X - AXB = C, obtains an explicit solution of the equation by means of characteristic polynomial, and then studies the quaternion matrix equation X - A X B = C, characterizes the existence of a solution to the matrix equation, and derives closed-form solutions of the matrix equation in explicit forms by means of real representations of quaternion matrices. This paper also gives an application to the complex matrix equation X - AXB =C.
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.
基金Supported by the National Natural Science Foundation of China(Grant No.11971294)。
文摘This paper studies a system of three Sylvester-type quaternion matrix equations with ten variables A_(i)X_(i)+Y_iB_(i)+C_(i)Z_(i)D_(i)+F_(i)Z_(i+1)G_(i)=E_(i),i=1,3^-.We derive some necessary and sufficient conditions for the existence of a solution to this system in terms of ranks and Moore–Penrose inverses of the matrices involved.We present the general solution to the system when the solvability conditions are satisfied.As applications of this system,we provide some solvability conditions and general solutions to some systems of quaternion matrix equations involvingφ-Hermicity.Moreover,we give some numerical examples to illustrate our results.The findings of this paper extend some known results in the literature.
文摘This paper derives a theorem of generalized singular value decomposition of quaternion matrices （QGSVD）,studies the solution of general quaternion matrix equation AXB -CYD= E,and obtains quaternionic Roth＇s theorem. This paper also suggests sufficient and necessary conditions for the existence and uniqueness of solutions and explicit forms of the solutions of the equation.
