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