Matrix left symmetry factor and its applications in generalized inverses AT,S(2,4)

In this paper, we propose some definitions about matrix symmetry factors and discuss the construction of matrix left symmetry factor in detail. The explicit expression of the generalized inverses AT,S(2,4), which is a {2, 4}-inverses of A having the prescribed rang T and null space S  , is derived. Furthermore, using the expression AT,S(2,4), we get the corresponding results for six important generalized inverses.