| 矩阵右半张量积的加权Drazin逆的反序律 |
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| 引用本文： | 宋彩芹,赵建立.矩阵右半张量积的加权Drazin逆的反序律[J].淮海工学院学报,2009,18(1):4-6. |
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| 作者姓名： | 宋彩芹 赵建立 |
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| 作者单位： | 聊城大学,数学科学学院,山东,聊城,252059
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| 摘 要： | 利用矩阵的秩方法，定义了矩阵右半张量积的加权Drazin逆的反序律（Bd，w2×Ip）＊Ad，w1=（Bd,w2×Ip）W2W1Ad,w1，并且给出矩阵右半张量积加权Drazin逆（A⊙B）d,1=（Bd,w2×Ip）＊Ad,w1成立的充要条件．给出当矩阵A，B都是方阵和矩阵W1，W2都是单位矩阵时，由上述结果可以直接得到Drazin逆反序律（A⊙B）d=（Bd×Ip）A。成立的充要条件．
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| 关 键 词： | Moore—Penrose逆 加权Drazin逆 指标 反序律 矩阵右半张量积 |
Reverse Order Law for the Weighted Drazin Inverse of a Matrix Right Semi-tensor Product |
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| SONG Cai-qin,ZHAO Jian-li.Reverse Order Law for the Weighted Drazin Inverse of a Matrix Right Semi-tensor Product[J].Journal of Huaihai Institute of Technology:Natural Sciences Edition,2009,18(1):4-6. |
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| Authors: | SONG Cai-qin ZHAO Jian-li |
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| Affiliation: | School of Mathematics Science;Liaocheng University;Liaocheng 252059;China |
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| Abstract: | The rank methods of matrix are used to study the reverse order law for the generalized inverse of the matrices right semi-tensor product. Let （Bd,w2× Ip ） ＊ Ad,w1 = （Bd,w2×Ip） W2W1Ad,w1 be given. At the same time, a sufficient and necessary condition for the weighted Drazin inverse （A⊙B）d,I = （Bd,w2 ×Ip） ＊ Ad,w1 is given. Particularly, as matrix A and matrix B are square matrices, and matrix W1 and matrix W2 are identity matrices, a sufficient and necessary condition can be obtained directly for （A⊙B）d = （Bd×Ip）Ad to hold the Drazin inverse. |
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| Keywords: | Moore-Penrose inverse weighted Drazin inverse index reverse order law matrix right semi-tensor product |
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