| 除环上分块矩阵的指标和Drazin逆 |
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| 引用本文： | 谷德红,曹重光. 除环上分块矩阵的指标和Drazin逆[J]. 黑龙江大学自然科学学报, 2011, 28(2): 196-199 |
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| 作者姓名： | 谷德红 曹重光 |
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| 作者单位： | 黑龙江大学数学科学学院,哈尔滨,150080 |
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| 基金项目： | Supported by the National Science Foundation of China(10671026) |
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| 摘 要： | 设K为除环,Kmxn是K上所有mxn矩阵的集合.设A∈Kmxn,满足rank(As+1)=rank(As)的最小非负整数s称为A的指标,记作Ind(A)=s.设A∈Kmxn,Ind(A)=s,如果X∈Knxn满足以下方程:(1)AXA=X(2)AX=XA(3)As+1X=As,则称为X为A的Drazin逆,记作X=AD...
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| 关 键 词： | 除环 指标 Drazin逆 |
The index and the Drazin inverse of partitioned matrices over skew fields |
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| GU De-hong,CAO Chong-guang. The index and the Drazin inverse of partitioned matrices over skew fields[J]. Journal of Natural Science of Heilongjiang University, 2011, 28(2): 196-199 |
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| Authors: | GU De-hong CAO Chong-guang |
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| Affiliation: | GU De-hong,CAO Chong-guang (School of Mathematical Science,Heilongjiang University,Harbin 150080,China) |
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| Abstract: | Let Km×n be the set of all m×n matrices over a skew field K. The smallest nonnegative integer s satisfying rank (As+1) = rank (As) is called the index of the matrix A in Kmxn, and is denoted by Ind(A) =s.Let A∈Kn×n, if X∈Kn×n satisfies the equations: (1)XAX=X; (2)AX=XA; (3)As+1X = As, where Ind(A) = s, then X is called the Drazin inverse of A, and is denoted by X = AD.The index and the Drazin inverse of partitioned matrix (A B O C) over a skew field are researched by using the method of Fitting factorization. |
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| Keywords: | skew field index Drazin inverse |
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