On the solutions of the quaternion interval systems [x] = [A] [x] + [b]

Bolat C., Ipek A.

Applied Mathematics and Computation, vol.244, pp.375-381, 2014 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 244
  • Publication Date: 2014
  • Doi Number: 10.1016/j.amc.2014.06.106
  • Journal Name: Applied Mathematics and Computation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.375-381
  • Keywords: Intervals, Quaternions, The systems of equations
  • Hacettepe University Affiliated: No


It is known that linear matrix equations have been one of the main topics in matrix theory and its applications. The primary work in the investigation of a matrix equation (system) is to give solvability conditions and general solutions to the equation(s). In the present paper, for the quaternion interval system of the equations defined by [x]=[A][x]+[b], where [A] is a quaternion interval matrix and [b] and [x] are quaternion interval vectors, we derive a necessary and sufficient criterion for the existence of solutions [x]. Thus, we reduce the existence of a solution of this system in quaternion interval arithmetic to the existence of a solution of a system in real interval arithmetic. © 2014 Elsevier Inc. All rights reserved.