广义逆矩阵与相容线性方程组

广义逆矩阵与相容线性方程组

关键词: 广义逆矩阵；极小范数解；线性方程组

Generalized Inverse Matrix and

Compatible Linear Equations

Abstract: This paper systematically discussed the definition, nature and calculation of two kinds of generalized inverse matrix related to the compatible linear equations, and their relations with the compatible linear equations. The preface gave the definition and introduced history, background of development and significance of generalized inverse matrix. The first chapter, from the development process of generalized inverse, discussed all kinds of definition of generalized inverse determined by the Moore - Penrose equations. The second chapter discussed the definition and nature of dashes inverse A in generalized inverse as well as its application in compatible linear equations. The third chapter discussed the definition and calculation of the minimum norm inverse A in generalized inverse, as well as the Minimal Norm Solution of its compatible linear equations Ax = b. The whole text completely provided the definition, nature and computation of two kinds of generalized inverse matrix related to the compatible linear equation and its application in the compatible linear equations.

Key words: generalized inverse matrix; Minimal Norm Solution; linear equations