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J4 ›› 2011, Vol. 46 ›› Issue (4): 90-92.

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关于矩阵多项式秩的二个恒等式

左可正   

  1. 湖北师范学院数学系, 湖北 黄石 435002
  • 收稿日期:2010-04-27 发布日期:2011-04-21
  • 作者简介:左可正(1962- ),男,教授,研究方向为矩阵分析与代数学. Email: xiangzuo28@163.com.

Two equalities on the rank of polynomial of matrices

ZUO Ke-zheng   

  1. Department of Mathematics, Hubei Normal University, Huangshi 435002, Hubei, China
  • Received:2010-04-27 Published:2011-04-21

摘要:

利用分块矩阵的初等变换,证明了矩阵A的s个多项式秩的和的二个恒等式,其结果推广了相关的的结论。

关键词: 矩阵多项式;矩阵的秩;互素多项式;极小多项式

Abstract:

 By using the elementary transformations of block matrix, two equalities of the rank of the sum of s numbers of polynomials of a matrix A is proved. The results generalize related results.

Key words: matrix polynomial; rank of matrix; coprime polynomial; minimal polynomial

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