Least-squares bihermitian and skew bihermitian solutions of the quaternion matrix equationAXB = C

A New Method of Solving Special Solutions of Quaternion Generalized Lyapunov Matrix Equation

“…Matrix equation is one of the important research fields of numerical algebra, and the research on quaternion matrix equation also has been widely concerned by scholars. For example, Kyrchei studied the least-norm of the general solution to some system of quaternion matrix equations and its determinantal representations [17] and Cramers rules for Sylvester quaternion matrix equation and its special cases [18], Liu and Wang studied the solvability conditions and the formula of the general solution to a Sylvester-like quaternion matrix Equation [19], Mehany and Wang investigated the solvability conditions and the general solution of three symmetrical systems of coupled Sylvester-like quaternion matrix Equations [20], Jiang and Ling studied closed-form solutions of the quaternion matrix equation A X − XB = C in explicit forms [21], Wang studied the bisymmetric and central symmetric solutions of quaternion matrix Equations [22], Zhang studied the least squares biHermitian solutions and oblique biHermitian solutions of quaternion matrix Equations [23].…”