| 一类矩阵的对角化与秩的恒等式 |
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| 引用本文： | 黄弘.一类矩阵的对角化与秩的恒等式[J].山西师范大学学报,2010,24(1):21-24. |
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| 作者姓名： | 黄弘 |
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| 作者单位： | 孝感学院数学系,湖北,孝感,432100 |
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| 摘 要： | 利用矩阵对角化理论,给出了Sylvester不等式: rank A+rank B≤rank(AB)+n的取等号的一个充分条件, 同时得到了Frbenius不等式:rank(AB)+rank(BC)≤rank(ABC)+rank(B)等号成立的一个充分条件,并举例说明了它们的应用.
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| 关 键 词： | 矩阵对角化 矩阵的秩 m-幂等矩阵 m-对合矩阵 |
Rank Identity of a Class Matrices and Its Diagonalizability |
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| HUANG Hong.Rank Identity of a Class Matrices and Its Diagonalizability[J].Journal of Shanxi Teachers University,2010,24(1):21-24. |
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| Authors: | HUANG Hong |
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| Institution: | HUANG Hong(Department of Mathematics,Xiaogan University,Xiaogan 432000,Hubei,China) |
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| Abstract: | Applying the method of the diagonalizability,a sufficient condition is presented to the Sylvester inequality of matrix rank for the equality.At same time,we get a sufficient condition to the Frobenius inequality of matrix rank for the equality,and discuss the use of the identities about the rank of a class matrices by examples. |
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| Keywords: | diagonalizability rank of matrix m-idempotent matrix m-involutory matrix |
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