Explicit solutions of the Yang–Baxter-like matrix equation for a diagonalizable matrix with spectrum contained in {1, α, 0}

Dongmei Chen, Zhibing Chen and Xuerong Yong

Applied Mathematics and Computation, 2019, vol. 348, issue C, 523-530

Abstract: Let A ∈ Cl × l be a diagonalizable matrix with spectrum contained in the set {1, α, 0}. In this paper we derive a general and explicit expression for the solutions X of the Yang–Baxter-like matrix equation AXA=XAX. The idea involves partitioning the matrices to discuss four block-matrix equations and utilizing the eigen-properties of the matrices obtained. When A is an idempotent matrix, the result generates the formula obtained in Mansour et al. (2017). We give examples to illustrate the validity of the results obtained in this note.

Keywords: Yang–Baxter-like matrix equation; Eigenvalues; Diagonalizable matrix (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300318310865
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:348:y:2019:i:c:p:523-530

DOI: 10.1016/j.amc.2018.12.034

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().