广义二次矩阵和与积线性组合的秩与零度

J4 ›› 2013, Vol. 51 ›› Issue (02): 226-228.

广义二次矩阵和与积线性组合的秩与零度

刘淑媛¹, 陈梅香², 冯晓霞³, 杨忠鹏², 谢燕萍^4

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. 漳州师范学院数学与信息科学系| 福建漳州 363000； |4. 福建师范大学数学与计算机科学学院| 福州 350007

收稿日期:2012-11-20 出版日期:2013-03-26 发布日期:2013-03-27
通讯作者: 杨忠鹏 E-mail:yangzhongpeng@126.com

Rank and Nullity for Linear Combinations of Sumand Product of Generalized Quadratic Matrices

LIU Shu yuan¹, |CHEN Mei xiang², |FENG Xiao xia³, |YANG Zhong peng², XIE Yan ping⁴

1. |Department of Basic Course, Jilin Business and Technology College, Changchun 130062, China;
2. Department of Mathematics, Putian University, Putian 351100, Fujian Province, China|
3. Department of Mathematics and Information Science, Zhangzhou Normal University, Zhangzhou 363000, Fujian Province, China;
4. College of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China

Received:2012-11-20 Online:2013-03-26 Published:2013-03-27
Contact: YANG Zhong peng E-mail:yangzhongpeng@126.com

摘要/Abstract

摘要：

应用广义二次矩阵与幂等矩阵互为确定的关系，证明了在某种条件下广义二次矩阵和与积的线性组合的秩与其组合系数选择无关.

关键词: 广义二次矩阵；线性组合；秩；零度

Abstract:

Applying the mutual determined relationship between generalized quadratic matrices and idempotent ones, we proved that under a certain condition, rank and nullity for the linear combinations of sum and product of generalized quadratic matrices are independent of the choice of coefficients of the linear combinations.

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

中图分类号:

O151.21

刘淑媛, 陈梅香, 冯晓霞, 杨忠鹏, 谢燕萍. 广义二次矩阵和与积线性组合的秩与零度[J]. J4, 2013, 51(02): 226-228.

LIU Chu-Yuan, CHEN Mei-Xiang, FENG Xiao-Xia, YANG Zhong-Feng, XIE Yan-Ping. Rank and Nullity for Linear Combinations of Sumand Product of Generalized Quadratic Matrices[J]. J4, 2013, 51(02): 226-228.