Constraint generalized Sylvester matrix equations

Determinantal Representations of General and (Skew-)Hermitian Solutions to the Generalized Sylvester-Type Quaternion Matrix Equation

“…Systems of periodic discrete-time coupled Sylvester quaternion matrix equations [10], systems of quaternary coupled Sylvester-type real quaternion matrix equations [11], and optimal pole assignment of linear systems by the Sylvester matrix equations [12] have been explored. Some constraint generalized Sylvester matrix equations [13,14] were studied recently.…”

Least-Norm of the General Solution to Some System of Quaternion Matrix Equations and Its Determinantal Representations

“…Some recent work on generalized Sylvester matrix equations and their systems can be observed in [19][20][21][22][23][24][25][26][27][28][29][30][31]. In 2014, Bao [32] examined the least-norm and extremal ranks of the least square solution to the quaternion matrix equations…”

A Numerical Approach To Generalized Periodic Sylvester Matrix Equation

“…In the existing literature, several forms of matrix equations have been investigated [3][4][5][6][7], in which Sylvester matrix equations rouse more interest. For examples, the constrained generalized Sylvester matrix equation is considered in [8], the necessary and sufficient conditions for its solvability and the expression of its general solution when it is solvable are presented together. Reference [9] studied Sylvester matrix equations in the forms of AXB− CXD = E, AX − X T D = E and AXB − X T = E. An iterative method is constructed to solve the linear matrix equation AXB = C over skew-symmetric matrix in [10], Manuscript by which the solvability of the equation AXB = C over skew-symmetric matrix can be determined automatically.…”

“…In the existing literature, several forms of matrix equations have been investigated , in which Sylvester matrix equations rouse more interest. For examples, the constrained generalized Sylvester matrix equation is considered in , the necessary and sufficient conditions for its solvability and the expression of its general solution when it is solvable are presented together. Reference studied Sylvester matrix equations in the forms of A X B − C X D = E , A X − X T D = E and A X B − X T = E .…”