| 广义逆A(2)T,S的体积 |
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| 引用本文： | 王国荣,高璟.广义逆A(2)T,S的体积[J].上海师范大学学报(自然科学版),2006,35(1):16-21. |
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| 作者姓名： | 王国荣 高璟 |
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| 作者单位： | 1. 上海师范大学,数理信息学院,上海,200234
2. 上海应用技术学院,上海,200235 |
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| 基金项目： | This work is supported by the National Natural Science Foundation of China, Science and Technology Foundation of Shanghai and Shanghai Higher Education Project, and the Special Funds for Major Specialities of Shanghai Education Committee. Supported by the Science and Technology Foundation Project QJ2004 - 08 of Shanghai Institute of Technology. |
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| 摘 要： | 研究了广义逆A（T,S）^（2）是的体积，在不必首先计算出广义逆A（T,S）^（2）的前提下，导出了广义逆A（T,S）^（2）的体积表示，推广了文献3]中的结果．由此分别给出了A的加权Moore-Penrose逆，Drazin逆Ad及群逆Ag的体积表示式．
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| 关 键 词： | 体积 广义逆A(2)T S 主角 |
| 文章编号： | 1000-5137(2006)01-0016-06 |
| 收稿时间： | 11 12 2005 12:00AM |
| 修稿时间： | 2005年11月12 |
A volume associated with generalized inverse A(2)T,S |
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| WANG Guo-rong,GAO Jing.A volume associated with generalized inverse A(2)T,S[J].Journal of Shanghai Normal University(Natural Sciences),2006,35(1):16-21. |
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| Authors: | WANG Guo-rong GAO Jing |
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| Affiliation: | 1. Mathmatics and Sciences College, Shanghai Normal University, Shanghai 200234, China; 2. Shanghai Institute of Technology, Shanghai 200235, China |
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| Abstract: | The volume ofa matrixA ∈ Rm×nr ,denoted by vol (A) ,is defined as the product of its nonzero singular values. So the volume of the Moore-Penrose inverse A + is given directly by vol(A +) =1-vol(A).It means that the expression of the volume of the Moore-Penrose inverse A + can be obtained without calculating the Moore-Penrose inverse A+ firstly. This paper deals with the representation of the volume of the generalized inverseA(2)T,S without calculating the generalized inverse a(2)T,S firstly. The expressions of the volumes of other generalized inverses, includeing the weighted M-P inverse, the group inverse, and the Drazin inverse, are provided. The main results are also the generalization of the results proposed by 3]. |
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| Keywords: | volume generalized inverse A(2)T S principal angles |
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