| 关于A+,A+MN的表达式及其应用 |
| |
| 引用本文： | 蔡静,陈果良.关于A+,A+MN的表达式及其应用[J].高等学校计算数学学报,2002,24(4):320-326. |
| |
| 作者姓名： | 蔡静 陈果良 |
| |
| 作者单位： | 1. 湖州师范学院数学系,湖州,313000;华东师范大学数学系,上海,200062
2. 华东师范大学数学系,上海,200062 |
| |
| 基金项目： | 国家自然科学基金，上海市学科科研项目，19871029，，， |
| |
| 摘 要： | For A ∈ Cm×nr, let M and N be Hermitian positive definite matrices oforder m and n respectively. We derived the representation of the Moore-PenroseA+MN in terms of maximal nonsin-inverse A+ and weighted Moore-Penrose inverse +gular submatrices of A. In our notation,A+ = | detAplq]|2A+pq1/vol2(A) (p,q)∈N(A)AM+N = 1/vol2(A)(p,q)∈N(A) |detAp|q]|2N-1/2A+pqM1/2where A=M1/2 AN -1/2. From this, we propose a new method to calculate A+A+MN. The results generalize that of Moore-Penrose inverse in 2]3].
|
| 关 键 词： | 表达式 矩阵 对称正定阵 |
ON THE REPRESENTATION OF A+ ,A+MN AND ITS APPLICATIONS |
| |
| Abstract.ON THE REPRESENTATION OF A+ ,A+MN AND ITS APPLICATIONS[J].Numerical Mathematics A Journal of Chinese Universities,2002,24(4):320-326. |
| |
| Authors: | Abstract |
| |
| Abstract: | For A , let M and N be Hermitian positive definite matrices of order m and n respectively. We derived the representation of the Moore-Penrose inverse A+ and weighted Moore-Penrose inverse AMN+ terms of maximal nonsin-gular submatrices of A. In our notation,where A = M1/2 AN-1/2 . From this, we propose a new method to calculate A+ , AMN+, The results generalize that of Moore-Penrose inverse in 233. |
| |
| Keywords: | full rankfactorization maximal nonsingular submatrix |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
