二次矩阵广义Jordan积秩的不变性

Journal of Jilin University Science Edition

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Invariance of Rank for Generalized Jordan Products of Quadratic Matrix

LV Hongbin¹, YANG Zhongpeng², CHEN Meixiang², FENG Xiaoxia ³

1. School of Mathematics and Statistics, Beihua University, Jilin 132013, Jilin Province, China;2. College of Mathematics, Putian University, Putian 351100, Fujian Province, China;3. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, Fujian Province, China

Received:2017-05-26 Online:2017-11-26 Published:2017-11-29
Contact: YANG Zhongpeng E-mail:yangzhongpeng@126.com

Abstract

Abstract: By gaving mutual determination relationship between quadratic matrix and quadratic polynomial, we obtained invariance of rank for generalized Jordan products of quadratic matrix and a new rank equations associated with quadratic matrix by means of matrix transformation. The results summarized and generalized the relevant results of the rank equations such as the (scalar) idempotent matrix, (scalar) involutory matrix, etc.

Key words: rank, quadratic matrix, invariance, Jordan product of matrix

CLC Number:

O151.21

LV Hongbin, YANG Zhongpeng, CHEN Meixiang, FENG Xiaoxia. Invariance of Rank for Generalized Jordan Products of Quadratic Matrix[J].Journal of Jilin University Science Edition, 2017, 55(06): 1416-1424.

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Invariance of Rank for Generalized Jordan Products of Quadratic Matrix

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