In this paper,the generalized inverse eigenvalue problem for the（P,Q）-conjugate matrices and the associated approximation problem are discussed by using generalized singular value decomposition（GSVD）.Moreover,the ...In this paper,the generalized inverse eigenvalue problem for the（P,Q）-conjugate matrices and the associated approximation problem are discussed by using generalized singular value decomposition（GSVD）.Moreover,the least residual problem of the above generalized inverse eigenvalue problem is studied by using the canonical correlation decomposition（CCD）.The solutions to these problems are derived.Some numerical examples are given to illustrate the main results.展开更多
Generally, the least-squares problem can be solved by the normal equation. Based on the projection theorem, we propose a direct method to investigate the maximal and minimal ranks and inertias of the least-squares sol...Generally, the least-squares problem can be solved by the normal equation. Based on the projection theorem, we propose a direct method to investigate the maximal and minimal ranks and inertias of the least-squares solutions of matrix equation AXB = C under Hermitian constraint, and the corresponding formulas for calculating the rank and inertia are derived.展开更多
Let A be an arbitrary square matrix,then equation AXA=XAX with unknown X is called Yang-Baxter matrix equation.It is difficult to find all the solutions of this equation for any given A.In this paper,the relations bet...Let A be an arbitrary square matrix,then equation AXA=XAX with unknown X is called Yang-Baxter matrix equation.It is difficult to find all the solutions of this equation for any given A.In this paper,the relations between the matrices A and B are established via solving the associated rank optimization problem,where B=AXA=XAX,and some analytical formulas are derived,which may be useful for finding all the solutions and analyzing the structures of the solutions of the above Yang-Baxter matrix equation.展开更多
基金Supported by the Key Discipline Construction Project of Tianshui Normal University
文摘In this paper,the generalized inverse eigenvalue problem for the（P,Q）-conjugate matrices and the associated approximation problem are discussed by using generalized singular value decomposition（GSVD）.Moreover,the least residual problem of the above generalized inverse eigenvalue problem is studied by using the canonical correlation decomposition（CCD）.The solutions to these problems are derived.Some numerical examples are given to illustrate the main results.
基金Supported by the Science Foundation Project of Tianshui Normal University(TSA1315)
文摘Generally, the least-squares problem can be solved by the normal equation. Based on the projection theorem, we propose a direct method to investigate the maximal and minimal ranks and inertias of the least-squares solutions of matrix equation AXB = C under Hermitian constraint, and the corresponding formulas for calculating the rank and inertia are derived.
基金Supported by the National Natural Science Foundation of China(11961057)the Science and Technology Project of Gansu Province(21JR1RE287 and 2021B-221)+2 种基金the Fuxi Scientific Research Innovation Team of Tianshui Normal University(FXD2020-03)the Science Foundation(CXT2019-36 and CXJ2020-11)the Education and Teaching Reform Project of Tianshui Normal University(JY202004 and JY203008)。
文摘Let A be an arbitrary square matrix,then equation AXA=XAX with unknown X is called Yang-Baxter matrix equation.It is difficult to find all the solutions of this equation for any given A.In this paper,the relations between the matrices A and B are established via solving the associated rank optimization problem,where B=AXA=XAX,and some analytical formulas are derived,which may be useful for finding all the solutions and analyzing the structures of the solutions of the above Yang-Baxter matrix equation.
