Used The Generalized Inverse Of The Regular Inverse Said And Application,

Through comparing the exist condition of Boot-Duffin inverse and generalized Boot-Duffin inverse, we establish the relationship between the inverse and other common generalized inverses, such as Drazin inverse, Group inverse , and give the following explicit formulas:And we also guess and prove the following two explicit formulas of Moore-Pemose inverse :Usually AT,S(2) contains Moore-Penrose inverse , Drazin inverse, Group inverse , Boot-Duffin inverse and generalized Boot-Duffin inverse .In this paper , we also consider quasi-commuting inverses which is defined by Erdelyi in [2.12] , and we shows that quasi-commuting inverses are also special cases of complementary generalized inverse .Then we give perturbation analysis and the iterative computing methods of complementary generalized inverse under certain condition .Using the two explicit formulas of Moore-Penrose inverse , we get; and A is a L-zero matrix .(i.e. the case of generalized Boot-Duffin inverse . )Then ,through using two projections , we present the three explicit formulas of the generalized inverse AT,S(2) :(where A Cmxn)and we apply this result to solve restricted linear equations .At last ,we deals with the case when the α-β generalized inverse A(-1)α,β is a linear transformation , in which case we established the characterization of the α-β generalized inverse, and we also give several sufficient conditions that the reverse law holds,...