| 域上矩阵积的广义逆及自反广义逆的逆反律 |
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| 引用本文： | 刘淑丹,游宏.域上矩阵积的广义逆及自反广义逆的逆反律[J].数学年刊A辑(中文版),2004(4). |
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| 作者姓名： | 刘淑丹 游宏 |
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| 作者单位： | 哈尔滨工业大学数学系，哈尔滨工业大学数学系 哈尔滨 150001，哈尔滨 150001 |
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| 基金项目： | 国家自然科学基金，黑龙江省自然科学基金 |
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| 摘 要： | 令A,B是任意域上的矩阵且使得AB有意义。本文研究了AB的广义逆、自反广义逆与A,B的广义逆、自反广义逆的积之间的关系,得到了B{1}A{1}(AB){1},B{1}A{1}=(AB){1},B{1,2}A{1,2}(AB){1,2}和B{1,2}A{1,2}=(AB){1,2}成立的一些充要条件。
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| 关 键 词： | g-逆 自反g-逆 二个矩阵的积 域 |
REVERSE ORDER LAW FOR GENERALIZED INVERSES AND REFLEXIVE GENERALIZED INVERSES OF PRODUCTS OF MATRICES OVER ARBITRARY FIELDS |
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| LIU Shudan YOU Hong.REVERSE ORDER LAW FOR GENERALIZED INVERSES AND REFLEXIVE GENERALIZED INVERSES OF PRODUCTS OF MATRICES OVER ARBITRARY FIELDS[J].Chinese Annals of Mathematics,2004(4). |
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| Authors: | LIU Shudan YOU Hong |
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| Affiliation: | LIU Shudan~* YOU Hong~* *Department of Mathematics,Harbin Institute of Technology,Harbin 150001,China. |
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| Abstract: | Let A and B be matrices over an arbitrary field such that AB exists. The relationship between generalized inverses, reflexive generalized inverses of AB and the products of generalized inverses, reflexive generalized inverses of A, B have been studied in this paper. The authors derive some necessary and sufficient conditions for B{1}A{1} (AB){1},B{1}A{1}=(AB){1}, B{1, 2}A{1, 2} (AB){1, 2} and B{1, 2}A{1, 2}=(AB){1, 2}. |
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| Keywords: | g-inverse Reflexive g-inverse Product of two matrices Field |
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