Solution to a system of real quaternion matrix equations encompassing η-Hermicity

Cramer’s rules for the system of quaternion matrix equations withη-Hermicity

“…Denote is the qth row of b X g 1 :¼ X g 1 A gà 2 H. Construct the matrix X ¼ x qj À Á such that x qj is determined in (36) and denote b X :¼ T à A 2 X. From these denotations and the equation (35), it follows…”

“…An iterative algorithm for determining g (-skew)-Hermitian least-squares solutions to the quaternion matrix equation 3was established in [27]. For more related papers on g-Hermicity and its generalization, /-Hermicity, one may refer to [28][29][30][31][32][33][34][35][36][37][38].…”

Determinantal Representations of General and (Skew-)Hermitian Solutions to the Generalized Sylvester-Type Quaternion Matrix Equation

“…The expressions of the least squares solutions to some Sylvester-type matrix equations over nonsplit quaternion algebra [19] and Hermitian solutions over a split quaternion algebra [20] were derived. Solvability conditions and general solution for some generalized Sylvester real quaternion matrix equations involving -Hermicity were given in [21,22].…”

Least squares X=±Xη* solutions to split quaternion matrix equation AXAη*=B

“…The concept of -(anti-)Hermitian matrix is a more generalized concept comparing with (skew-)Hermitian matrix. This kind of matrices over H have been widely investigated (see, eg, previous studies 1,7,8,13,17,19,21,25 ). For instance, a singular value decomposition for -Hermitian matrices over H, 7 -(anti-)Hermitian solution to quaternion matrix equations such as AX+(AX) * +BYB * +CZC * = D, AX = B, AXB = C, AXA * = B, EXE * +FYF * = H (see, eg, previous studies 8,13,25 ), the least squares -(anti-)Hermitian solution to AXB + CYD = E, AXB + CXD = E, AXB = C (see, eg, previous studies 1,19,21 ), and other kinds of equations and solutions (see, eg, previous studies 2, 3,18,22,23,26 ).…”