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

Bolat, CennetIpek, Ahmet2024-09-182024-09-1820140096-30031873-5649https://doi.org/10.1016/j.amc.2014.06.106https://hdl.handle.net/20.500.12483/10686It 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. (C) 2014 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/closedAccessIntervalsQuaternionsThe systems of equationsOn the solutions of the quaternion interval systems [x] = [A][x] plus [b]Article24437538110.1016/j.amc.2014.06.1062-s2.0-84905058229Q1WOS:000342265700032Q1