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

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  • Chen, Dongmei
  • Chen, Zhibing
  • Yong, Xuerong

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.

Suggested Citation

  • Chen, Dongmei & Chen, Zhibing & Yong, Xuerong, 2019. "Explicit solutions of the Yang–Baxter-like matrix equation for a diagonalizable matrix with spectrum contained in {1, α, 0}," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 523-530.
    • Handle: RePEc:eee:apmaco:v:348:y:2019:i:c:p:523-530
    DOI: 10.1016/j.amc.2018.12.034
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