ABSTRACT This paper studies several special least squares solutions of complex split quaternion matrix equations and . First of all, for the complex split quaternion matrix, we define its real representation by applying the semi‐tensor product (STP) and study its properties. Then, according to these properties, the MP inverse, the Kronecker product and the operator, we provide expressions for three special types of least squares solutions and their corresponding minimum norm solutions of and . Subsequently, we propose real algorithms for above minimum norm solutions and verify their efficiency by several numerical experiments. Eventually, as an application, we employ the least squares pure imaginary solution of to handle the problem of color image restoration.
Zhang et al. (Fri,) studied this question.