摘要
在因式分解范畴中定义态射的因式分解广义逆,给出了它的显形式,讨论了其唯一性.应用于范畴C^m×n中,态射A:m→n的满秩分解(A_1,r,A_2)可刻划A的具有指定值域和零空间的(1,2)逆,并给出了具有指定值域和零空间的(1,2)逆表成因式分解广义逆的充要条件.
In this paper we defined the generalized inverse with factorization of morphism in a category with factorization, gave out its explict formulas, discussed its uniqueness. Applying to the category Cm×n,we use the full-rank factoriza tion of matrix A to characterize the {1,2}-inverse of A with prescribed range and null space and get a necessary and sufficient condition for a {1,2}-inverse with prescribed range and null space can be expressed as a generalized inverse with factorization.
