环上二阶反三角块阵的群逆

Group Inverses of Some Anti-triangular Block Matrices over a Ring

研究环上几类二阶反三角块阵的群逆.通过一般环上矩阵群逆存在的条件,利用环上矩阵群逆的各种性质,讨论这些矩阵群逆的存在性,给出其充要条件,在群逆存在时给出确切的群逆表达式,并给出具体例子.推广了相应文献的结果.

The group inverses of some kinds of second-order anti-triangular block matrices are studied over a ring.Using the conditions of the existence of the group inverses of matrices and the properties of group inverses of matrices over a ring,we discuss the existence of their group inverses and give the necessary and sufficient conditions and the exact representation when the group inverses exist.This work generalize the results of the corresponding literature.