| 矩阵酉相抵的充分必要条件 |
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| 引用本文： | 侯识忠.矩阵酉相抵的充分必要条件[J].赣南师范学院学报,1993(Z2). |
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| 作者姓名： | 侯识忠 |
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| 作者单位： | 湖南师范大学 |
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| 摘 要： | 本文证明了下列结论:1.m×n矩阵A与B酉相抵的充分必要条件是tr((AA)~(*K))=tr((B B~*)~K), K=1,2,…,”,m2.m阶方阵A与B有相同奇异值的充分必要条件是tr((AA~*)~K)=tr((B B~*)~K),K=1,2,…,m。
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| 关 键 词： | 矩阵 酉相抵 迹 奇异值 |
THE NECESSARY AND SUFFICIENT CONDITION OF UOFFSETING OF MATRICES |
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| Hou Shizhong The south Campus of Hunan normal university.THE NECESSARY AND SUFFICIENT CONDITION OF UOFFSETING OF MATRICES[J].Journal of Gannan Teachers' College(Social Science(2)),1993(Z2). |
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| Authors: | Hou Shizhong The south Campus of Hunan normal university |
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| Institution: | Hou Shizhong The south Campus of Hunan normal university |
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| Abstract: | In this Paper, we prove the following theorems:
1 . The necessary and sufficient condition of U-offseting of mxn-fold matrix A、B is tr( (AA*)k)=tr( (BB*)k), K=l, 2, ……, m.
2, The necessary and sufficient condition of m-fold square matrix Aand B having the same singular value is tr ( (AA*) k) =tr( ( BB* ) k), K= 1 , 2, ……, m. |
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| Keywords: | square matrix U-offsetting singular |
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