广义二次矩阵线性组合的秩与零度

J4 ›› 2011, Vol. 49 ›› Issue (06): 993-996.

广义二次矩阵线性组合的秩与零度

刘淑媛¹, 杨忠鹏², 谢燕萍^2,3

1. 吉林工商学院基础部, 长春 130062； 2. 莆田学院数学系, 福建莆田 351100；3. 福建师范大学数学与计算机科学学院, 福州 350007

收稿日期:2011-05-15 出版日期:2011-11-26 发布日期:2011-11-28
通讯作者: 杨忠鹏 E-mail:yangzhongpeng@126.com.

Rank and Nullity of Linear Combinationsof Generalized Quadratic Matrices

LIU Shuyuan¹, YANG Zhongpeng², XIE Yanping^2,3

1. Department of Foundation, Jilin Business and Technology College, Changchun 130062, China;2. Department of Mathematics, Putian Universtiy, Putian 351100, Fujian Province, China;3. College of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China

Received:2011-05-15 Online:2011-11-26 Published:2011-11-28
Contact: YANG Zhongpeng E-mail:yangzhongpeng@126.com.

摘要/Abstract

摘要：

利用广义二次矩阵与幂等矩阵的关系及幂等矩阵线性组合的秩及零度的不变性, 证明了广义二次矩阵某些线性组合的秩及零度与其线性组合系数的选择是无关的, 从而概括并推广了数量幂等矩阵、数量对合矩阵、二次矩阵线性组合的秩及零度的一些相关结果.

关键词: 广义二次矩阵；线性组合；秩；零度

Abstract:

By the relation of generalized quadratic matrices to idempotent matrices and the known results on rank and nullity for linear combinations of idempotent matrices, we studied the invariance of rank and nullity for linear combinations of generalized quadratic matrices, which unified and generalized the related results in literature on rank and nullity for linear combinations of scalarpotent matrices, scalarinvolutory matrices and quadratic matrices.

Key words: generalized quadratic matrix, linear combination, rank, nullity

中图分类号:

O151.21

刘淑媛, 杨忠鹏, 谢燕萍. 广义二次矩阵线性组合的秩与零度[J]. J4, 2011, 49(06): 993-996.

LIU Chu-Yuan, YANG Zhong-Feng, XIE Yan-Ping-. Rank and Nullity of Linear Combinationsof Generalized Quadratic Matrices[J]. J4, 2011, 49(06): 993-996.