有限维欧氏空间上线性映射的广义逆

Generalized Inverse of Linear Mapping in Euclidean Space

线性映射和广义逆是高等代数很重要的研究对象.线性变换的广义逆被普遍研究,而线性映射的广义逆性质研究地很少.应用共轭映射的性质,给出了欧式空间商线性映射的广义逆的定义,并研究它的若干性质。这些性质对学生的学习有一定的帮助作用.

Linear maps and generalized inverses are very important objects in Higher Algebra. Some prop- erties of generalized inverses of linear translations are studied in many papers. However, there are few researches about generalized inverses of linear maps~ With the conjugation of matrices, we give the defi- nition of the generalized inverse of a linear mapping in Euclidean Space and study its some properties. They can help for study and applications of matrix theories.