| 除环上分块矩阵的秩 |
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| 引用本文： | 李桃生,黄振东,沈婧芳.除环上分块矩阵的秩[J].黑龙江大学自然科学学报,2004,21(4):31-34. |
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| 作者姓名： | 李桃生 黄振东 沈婧芳 |
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| 作者单位： | 华中师范大学,数学与统计学学院,湖北,武汉,430079 |
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| 摘 要： | 除环上有零对象的矩阵范畴是Abel范畴,在这个范畴中,解齐次线性方程组(A,B)X=0(或者X
AB]=0)与求态射{A,B}的推出(或者求态射{A,B}的拉回)有着密切的关系.讨论除环上齐次线性方程组(A,B)X=0和X
AB]=0;研究除环上有关分块矩阵之间的关系,得到了一些关于分块矩阵与其中子矩阵的秩的有关公式.
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| 关 键 词： | 除环 分块矩阵 Abel范畴 推出 拉回 |
The rank of block matrix over division ring |
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| LI Tao-sheng,HUANG Zhen-dong,SHEN Jing-fang.The rank of block matrix over division ring[J].Journal of Natural Science of Heilongjiang University,2004,21(4):31-34. |
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| Authors: | LI Tao-sheng HUANG Zhen-dong SHEN Jing-fang |
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| Abstract: | Matrix category with a zero object over division ring is an Abel category. In this category, solving the homo- " # A geneous linear equation set ( A, B )X = 0(or X = 0) have close contact with seeking the pushout for morphisms B " # A {A,B}(or the pullback for morphisms {A,B}) .The homogeneous linear equation sets ( A, B )X = 0 and X = 0 are B discussed and the relationship between block matrixes are studied over division ring. Some formulas of rank about block matrixes and the submatrixes over division ring are given. |
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| Keywords: | division ring block matrix Abel categories pushout pullback |
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