Extreme ranks of a linear quaternion matrix expression subject to triple quaternion matrix equations with applications

Least-norm and Extremal Ranks of the Least Square Solution to the Quaternion Matrix Equation AXB=C Subject to Two Equations

“…The study on the possible ranks of matrix equations can be traced back to 1970s (see [1,[18][19][20]29]). Recently, the extremal ranks, i.e., maximal and minimal ranks, of some matrix expressions have found many applications in control theory (see [2,4]), statistics, and economics (see [22,23,28]), and hence this topic has been revisited in [3,15,[25][26][27][32][33][34][35].…”

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

“…(i) If rank A = r ≤ m < n, then by Theorem 3.2 we can represent the matrix A + by (9). Therefore, we obtain for all i = 1, .…”

“…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.…”

Maximal and Minimal Ranks of the Common Solution of Some Linear Matrix Equations over an Arbitrary Division Ring with Applications

“…Recently, Wang, Wu and Lin [19] presented some formulas of extreme ranks of a quaternion matrix expression A − A 3 X 1 B 3 − A 4 X 2 B 4 , where X 1 and X 2 are variant quaternion matrices, subject to two consistent systems of quaternion matrix equations A 1 X 1 = C 1 , X 1 B 1 = C 2 and A 2 X 2 = C 3 , X 2 B 2 = C 4 . Wang, Yu and Lin [20] established some formulas of extreme ranks of a quaternion matrix expression C 4 − A 4 XB 4 , where X is a variant quaternion matrix, subject to a consistent system of quaternion matrix equations…”