Two Classes Of Symplectic Matrices' Constrained Matrix Equation Problem And Their Optimal Approximations

strained matrix equation problems are getting extensive and profound, symplec-tic matrices have been wildly used in many fields such as mechanics,engineeringcalculation,optimal control and so on,and sympletic matrices'Constrained matrixequation problem presses for solution.In this paper,the constrained matrix equationproblem and the optimal approximation in solution set for any given matrix aresystematically studied for one class of symplectic orthogonal matrices and one classof symplectic matrices like I2n ? wwTJ. we mainly discuss the following problems:Problem I Given X ,find A∈S,such that AX = XΛProblem II Given ,find A∈S,such thatAX = BProblem III Given such thatwhere SE is the solution set of problem I , . is the Frobebius norm.The paper has three parts.In the first chapter,we mainly discussed the research in matrix inverse problemwhich had been done by progenitors and symbols,definitions and basic theoremsfor the paper.In the second chapter,we studied the necessary and su?cient conditions ofsolvability for the constrained matrix equation problem of one class of symplecticorthogonal matrices,presented the expression of general solution,and considered theoptimal approximation in corresponding solution set and presented some numericalexamples.In the third chapter,we studied the necessary and su?cient conditions of solv-ability for the constrained matrix equation problem of one class of symplectic ma-trices like I2n ? wwTJ,and considered the optimal approximation in corresponding solution set and presented the expression of general solution,and presented somenumerical example.