约束条件为双反对称非负定阵的矩阵方程AX=B的求解

Solution of Matrix Equation AX=B with Controlled Condition of Anti-bisymmetric Nonnegative Definite Matrices

矩阵方程AX=B的解历来是许多学科研究的重点.若不加入约束条件,则此方程无确定解.限定A为双反对称非负定矩阵,利用矩阵的奇异值分解讨论了当X,B∈Rn×n时AX=B存在双反对称非负定解的条件,并给出了通解的表达式,为进一步讨论矩阵方程AX=B奠定了基础.

The solution of matrix equation AX = B has been impertomt in many science research for which if no restricted control conditions are given, then no definite solutions exist. In this paper, using the decomposition of matrix, the canditions with which the eqution AX = B has anti - bisymmetric nonutgative definite solutions, where X, B ∈ R^n×n are discusstd and the expression of the solution is presented so it makes a theoretical foundation for further research to matrix equation AX = B.