The maximal rank of a kind of partial banded block matrix subject to linear equations
Dezhong Lian, John Y. Chiang · Filomat · 2013
We establish the formulas of the maximal rank of a 3x3 partial banded block matrix () where X, Y, and Z are three variant quaternion matrices subject to linear matrix equations A1X = C1, XB1 = C2, A2Y = D1, YB2 = D2, A3Z = E1, ZB3 = E2. In order to demonstrate the feasibility of the result obtained, we present a necessary and sufficient condition for the solvability to the cubic system A1X = C1, XB1 = C2, A2Y = D1, YB2 = D2, A3Z = E1, ZB3 = E2, XYZ = J over the quaternion algebra.