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January 26, 2026Journal of Algebra and Its Applications0 citations

Two-sided Linear Quaternionic Equations

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YCYulu ChenBLBowen LiuBWBin Wang

Key Points

  • The aim is to solve two-sided linear quaternionic equations using a new concept called discriminant space.
  • Introduced the concept of discriminant space.
  • Established criteria for the existence of solutions.
  • Developed methods to efficiently obtain all solutions.
  • Applied theories to general systems of two-sided linear quaternionic equations.
  • Considered equations with conjugate terms.
  • Provided sufficient and necessary criteria for solution existence.
  • Developed an efficient method for finding all solutions.
  • Established similar theories for systems and conjugate equations.

Abstract

This paper aims to solve two-sided linear quaternionic equations by introducing a new concept: discriminant space. We provide the sufficient and necessary criteria for the existence of the solutions and a method to obtain all solutions efficiently. Furthermore, the similar theories are established for systems of general two-sided linear quaternionic equations, and two-sided linear quaternionic equations with conjugate.

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Cite This Study

Chen et al. (2026) studied this question.

synapsesocial.com/papers/69770393722626c4468e8a09https://doi.org/10.1142/s0219498826400013
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