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

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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. 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

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

CLC Number: 

  • O151.21