| 一类紧凑格式的约束矩阵方程解的Cramer法则 |
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| 引用本文： | 王国荣,方茂中.一类紧凑格式的约束矩阵方程解的Cramer法则[J].黑龙江大学自然科学学报,2004,21(4):11-16. |
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| 作者姓名： | 王国荣 方茂中 |
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| 作者单位： | 上海师范大学,数理信息学院,上海,200234;上海师范大学,数理信息学院,上海,200234 |
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| 基金项目： | Supported by National Natural Science Foundation of China，Specialized Research Fund for the DoctoralProgram of High Eduction，Science and Technology Foundation of Shanghai，Shanghai Higher Eduction Project(03DZ04) |
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| 摘 要： | 证明了一类约束矩阵方程WAWXW~BW~=D,R(X)
R(X) R(AW)k1],N(X) N(W~B)k~2]有唯一解并给出其解的Cramer法则,其中A∈Cm×n,W∈Cn×m,Ind(AW)=k1,Ind(BW~)=k~1,B∈Cp×q,W~∈Cq×p,Ind(WA)=k2,Ind(W~B)=k~2,and
D∈Cn×p,R(D) R(WA)k2],N(D) N(BW~)k~1].
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| 关 键 词： | 紧凑的Cramer法则 W-Drazin逆 约束矩阵方程 指标 |
A more condensed Cramer rule for solution of the general restricted matrix equation |
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| WANG Guo-rong,FANG Mao-zhong.A more condensed Cramer rule for solution of the general restricted matrix equation[J].Journal of Natural Science of Heilongjiang University,2004,21(4):11-16. |
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| Authors: | WANG Guo-rong FANG Mao-zhong |
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| Abstract: | A more condensed Cramer rule for finding the unique W-weighted Drazin inverse solution of a class of restricted matrix equationWAWXW~BW~= D, R(X) CR(AW)k1], N(X) N(W~B)k2]is presented, and the results in Linear Algebra Appl. 116(1989)27, Appl. Math. Comput.125(2002)303] can be deduced from this paper. WhereA ∈ Cm×n ,W ∈ Cm×m, Ind(AW) = k1, B ∈ Cp×q ,W~∈ Cq×p, Ind(W~B) = k~2, and D ∈ Cn×p, R(D) R(WA)k2], N(D) N(BW~)k~1]. |
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| Keywords: | condensed Cramer rule W-weighted Drazin inverse restricted matrix equation index |
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