线性代数方程组的解的表示

The Expression of the Solution of the System of Linear Algebraic Equations

本文在R^(?)中讨论了线性代数方程组的形式解,给出了解存在唯一的充分必要条件。当解唯一时,此形式解便是经典解,当解不唯一时,此形式解为其最小范数解,此方法既便于理论分析,又便于数值计算。

In this paper, we give the expression of the solution of the system of linear algebraic equations, obtain the necessary and sufficient condition to the existence and the u-niqueness for the solution of the system. When it has more than one solution, the expression of the solution is its minimum norm solution. The method given in the paper is efficient to theoretic analysis, and convenient to numerical calculation.