江声远.因式分解广义逆[J].数学研究及应用,1991,11(3):343~347 |
因式分解广义逆 |
Generalized Inverses with Factorization |
投稿时间:1988-11-07 |
DOI:10.3770/j.issn:1000-341X.1991.03.005 |
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中文摘要: |
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Cm×n中,态射A:m→n的满秩分解(A1,r,A2)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. |
英文摘要: |
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. |
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