刘桂香.三矩阵乘积的(T,S,2)-逆的反序律[J].数学研究及应用,2003,23(4):731~736 |
三矩阵乘积的(T,S,2)-逆的反序律 |
The Reverse Order Law for (T,S,2)-Inverse of a Triple Matrix Product |
投稿时间:2001-02-12 |
DOI:10.3770/j.issn:1000-341X.2003.04.026 |
中文关键词: 矩阵乘积 (T S 2)-逆 反序律 |
英文关键词:matrix product (T S 2)-inverse reverse order law. |
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中文摘要: |
矩阵A的(T,S,2)-逆是指适合XAX=X,R(X)=T和N(X)=S的矩阵X,以矩阵的秩为工具,本文研究了三矩阵乘积的(T,S,2)-逆的反序律,给出了(ABC)(T4,S4)(2)=C(T3,S3)(2)B(T2,S2)(2)A(T1,S1)(2)的充要条件。 |
英文摘要: |
The (T, S,2)-inverse .AT,S(2) of a matrix A is matrix the X satisfying XAX = X,R(X) = T and N(X) = S . This paper deals with the reverse order law for (T,S,2)-inverse of a triple matrix product and proves the necessary and sufficient condition for (ABC)(T4,S4)(2)=C(T3,S3)(2)B(T2,S2)(2)A(T1,S1)(2). |
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