Cramer’s rule for some quaternion matrix equations

Explicit representation formulas for the minimum norm least squares solutions of some quaternion matrix equations

“…But in [24], we defined the row and column determinants and the double determinant of a square matrix over the quaternion skew field. As applications we obtained the determinantal representations of an inverse matrix by an analogue of the adjoint matrix in [24] and the Moore-Penrose inverse over quaternion skew field H in [25].…”

“…In recent years quaternion matrix equations have been investigated by many authors (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]). For example, Jiang et al [1] studied the solutions of the general quaternion matrix equation AXB − CYD = E, and Liu [3] studied the least squares Hermitian solution of the quaternion matrix equation (A H XA, B H XB) = (CD), Wang et al.…”

The Moore–Penrose inverses of matrices over quaternion polynomial rings

“…For matrices over commutative rings, it is well-known that the Moore-Penrose inverses have been defined and explored for many years (see, for example, [3,12,13,23]). This motivates us to consider the Moore-Penrose inverses of quaternion polynomial matrices.…”

Solving coupled matrix equations over generalized bisymmetric matrices

“…For example, Dehghan and Hajarian [19][20][21][22][23][24][25][26] proposed several efficient iterative algorithms for solving Sylvester matrix equations. In [27], an efficient method was proposed to find the generalized bisymmetric solutions of the matrix equation In [28], Cramer's rules for some quaternion matrix equations were presented within the framework of the theory of the column and row determinants. Kyrchei [29] considered systems of linear quaternionic equations and obtained Cramer's rules for right and left quaternionic systems of linear equations.…”