关于算子方程解的一个注记

A Note on Operator Equations

讨论了数域K上有限维空间X到有限维空间Y上的线性算子与Km×n上的矩阵间的相互关系和相互表示形式,证明了数域K上有限维空间上的算子方程与代数方程的相互表示形式和它们解的等价关系,进而得到有限维空间上线性算子的不动点问题与线性空间Kn上的线性方程组的相互表示形式及它们解的等价关系,从而把数域K上有限维空间上的算子方程和不动点问题转化为线性空间Kn上的线性方程组的求解问题.

The mutual relation and mutual representation form of linear operator X to Y where X and Y are finite dimension spaces and the matrix in K^m×n in number field K are discussed. The mutual representation form and the equivalence relation of the solutions of operator equations on finite dimension spaces and algebraic equation in number field K are proved. And then the mutual representation form and the equivalence relation of the solutions of the fixed point problem of linear operator on finite dimension space and linear system of equations on linear space K^n are obtained. So that the operator equation and the fixed point problem on finite dimension space in number field K can be transformed into the solving of linear system of equations on linear space K^n.