关于线性方程组Ax=b的解的注记

Note on Solution of a Linear Equations Ax=b

考虑了当b固定时 ,怎样的矩阵G ,使x =Gb是相容或不相容线性方程组Ax =b的极小范数解 ,最小二乘解 ,从而得到许多有益的结论 .

In this paper,we consider the minimal norm solution and the least squares solution of a linear equations Ax=b,where b≠0 is fixed,which is ignored in the books on generalized inverses of matrices.In this case,we give the general form of a matrix G such that x=Gb is m.n.and l.s.solutions of Ax=b,respectively.