矩阵方程A+X=AX广义三次矩阵解与绝对值方程的解#br#

Journal of Jilin University Science Edition ›› 2020, Vol. 58 ›› Issue (3): 498-506.

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Generalized Cubic Matrix Solutions to Matrix Equation A+X=AX and Solutions to Absolute Value Equation#br#

LV Hongbin¹, YANG Zhongpeng², CHEN Meixiang², WANG Xinchun³

1. School of Mathematics and Statistics, Beihua University, Jilin 132013, Jilin Province, China;
2. School of Mathematics and Finance, Putian University, Putian 351100, Fujian Province, China;
3. Teachers College, Eastern Liaoning University, Dandong 118003, Liaoning Province, China

Received:2019-12-02 Online:2020-05-26 Published:2020-05-20
Contact: YANG Zhongpeng E-mail:yangzhongpeng@126.com

Abstract

Abstract: Using Jordan standard form of generalized cubic matrix, we gave the necessary and sufficient conditions that the generalized cubic matrix solutions to the matrix equation AX=A+X existed and the form of the soluti
ons, and proved that the solutions to the absolute value equation Bx-|x|=b determined by the generalized cubic matrix solution B to AX=A+X existed.

Key words: , generalized cubic matrix, Jordan standard form, matrix equation, absolute value equation, solution

CLC Number:

O151.21

LV Hongbin, YANG Zhongpeng, CHEN Meixiang, WANG Xinchun. Generalized Cubic Matrix Solutions to Matrix Equation A+X=AX and Solutions to Absolute Value Equation#br#[J].Journal of Jilin University Science Edition, 2020, 58(3): 498-506.

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Generalized Cubic Matrix Solutions to Matrix Equation A+X=AX and Solutions to Absolute Value Equation#br#

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