The Anti-Bisymmetric Matrices Problem Of Matrix Equation AX=B

In this paper, we consider two problems, the expansion of anti-bisymmetric matrix andits optimal approximation with the linear constraint and the anti-bisymmetric optimalapproximation solution of matrix equation AX = B. In this paper, the anti-bisymmetricmatrices problem of matrix equation AX = B was researched for the first time.When we consider the expansion of anti-bisymmetric and its optimal approximationwith the linear constraint, we discuss the following problems and get two theorems:Problem 1Given X, B∈Rn×k and A0∈ASRq×q, find A∈BASRn×n, such thatProblem 2Given A~*∈Rn×n, find A∈S1 such thatwhere S1 is the solution set of Problem 1.When we consider the anti-bisymmetric optimal approximation solution of matrixequation AX = B, we discuss the following problems and get two theorems:Problem 3Given A, B∈Rk×n, find X∈BASRn×n, such thatAX = B.Problem 4Given X?∈Rn×n, find X∈S3 such thatwhere S3 is the solution set of Problem 3.At the end, we make a work summary of this paper and look forward to the followingresearch work about this subject.