| 两个分块矩阵相似性的研究 |
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| 引用本文： | 程士珍.两个分块矩阵相似性的研究[J].数学的实践与认识,2005,35(3):191-194. |
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| 作者姓名： | 程士珍 |
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| 作者单位： | 北京建筑工程学院基础部,北京,100044 |
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| 摘 要： | 给出两个分块矩阵相似的两个充分必要条件 .也就是说 ,如果两个方阵 A和 B在 A2 =0和 B2 =0的条件下 ,则两个分块矩阵 A C0 B 和 A 00 B 相似的充分必要条件是 :rank A C0 B =rank(A) +rank(B)和 AC +CB =0 .如果两个方阵 A和 B在 A2 =A和 B2 =B的条件下 ,则两个分块矩阵 A C0 B和 A 00 B 相似的充分必要条件是 :AC +CB =C.
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| 关 键 词： | 矩阵的秩 矩阵的值域 矩阵的逆 相似矩阵 |
| 修稿时间： | 2003年1月23日 |
A Study on the Similarity of the Block Matrices |
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| CHENG Shi-zhen.A Study on the Similarity of the Block Matrices[J].Mathematics in Practice and Theory,2005,35(3):191-194. |
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| Authors: | CHENG Shi-zhen |
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| Abstract: | In this note, we show the two necessary and sufficient conditions such that two block matrices are similar, that is, suppose that the two square matrices A and B satisfy A2=0 and B2=0. Show that the two block matrices AC=0B and A0=0B are similar if and only if rank AC=0B=rank(A) rank(B) and AC CB=0. Suppose that the two square matrices A and B satisfy A2=A and B2=B. Show that the two block matrices AC=0B and A0=0B are similar if and only if AC CB=C. |
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| Keywords: | rank of matrix range of matrix inverse of matrix similar matrices |
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