The uniqueness of expression for generalized quadratic matrices-Reference-Cited by-同舟云学术

The uniqueness of expression for generalized quadratic matrices

Published:2024-01-01 Issue:1 Volume:22 Page:
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Chen Meixiang¹,Yang Zhongpeng²,Chen Qinghua³

Affiliation:

1. Fujian Key Laboratory of Financial Information Processing, Putian University , Putian Fujian , 351100 , China

2. Key Laboratory of Applied Mathematics of Fujian Province University, Putian University , Putian Fujian , 351100 , China

3. School of Mathematics and Statistics, Fujian Normal University , Fuzhou Fujian , 350007 , China

Abstract

Abstract It is shown that the expression as

A 2 = α A + β P

{A}^{2}=\alpha A+\beta P

for generalized quadratic matrices is not unique by numerical examples. Then it is proven that the uniqueness of expression for generalized quadratic matrices is concerned not only with the properties of

but also with the rank of

. Furthermore, the sufficient and necessary conditions for the uniqueness of generalized quadratic matrices’expression are obtained. Finally, some related discussions about generalized quadratic matrices are also given.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/math-2023-0186/pdf

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