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

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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.

Abstract

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

CLC Number:

O151.21

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.

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Rank and Nullity of Linear Combinationsof Generalized Quadratic Matrices

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