Minor self conjugate (msc) and skewpositive semidefinite (ssd) solutions to the system of matrix equations over skew fields [A mn X nn =A mn ,B sn X nn =O sn ] are considered. Necessary and su...Minor self conjugate (msc) and skewpositive semidefinite (ssd) solutions to the system of matrix equations over skew fields [A mn X nn =A mn ,B sn X nn =O sn ] are considered. Necessary and sufficient conditions for the existence of and the expressions for the msc solutions and the ssd solutions are obtained for the system.展开更多
Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew...Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew field. The representations of such the solutions of the system are also derived.展开更多
In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skew field,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).A convenient,simple and practical method of s...In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skew field,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).A convenient,simple and practical method of solving(I)is also given.As a particular case,we also give a simple method of finding a system of fundamental solutions of a homogeneous system of right linear equations over a skew field.展开更多
A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.
The matrix equation A mn X ns B st =C over an arbitrary skew field is considered. A necessary and sufficient condition for the consistency and the expression for general solutions of the above mentioned matrix equatio...The matrix equation A mn X ns B st =C over an arbitrary skew field is considered. A necessary and sufficient condition for the consistency and the expression for general solutions of the above mentioned matrix equation are presented.Moreover,a practical method of solving one is also given.展开更多
A necessary and sufficient condition for the consisteney of the matrix equation AXB+CYD=E over an arbitrary skew field is given. Thus Roth's equivalence theorem is generalized.
文摘Minor self conjugate (msc) and skewpositive semidefinite (ssd) solutions to the system of matrix equations over skew fields [A mn X nn =A mn ,B sn X nn =O sn ] are considered. Necessary and sufficient conditions for the existence of and the expressions for the msc solutions and the ssd solutions are obtained for the system.
基金Supported by the National Natural Science Foundation of China(10471085)
文摘Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew field. The representations of such the solutions of the system are also derived.
文摘In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skew field,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).A convenient,simple and practical method of solving(I)is also given.As a particular case,we also give a simple method of finding a system of fundamental solutions of a homogeneous system of right linear equations over a skew field.
文摘A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.
文摘The matrix equation A mn X ns B st =C over an arbitrary skew field is considered. A necessary and sufficient condition for the consistency and the expression for general solutions of the above mentioned matrix equation are presented.Moreover,a practical method of solving one is also given.
文摘A necessary and sufficient condition for the consisteney of the matrix equation AXB+CYD=E over an arbitrary skew field is given. Thus Roth's equivalence theorem is generalized.
