We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
RANKS OF THE COMMON SOLUTION TO SOME QUATERNION MATRIX EQUATIONS WITH APPLICATIONS.
- Authors
WANG, Q. W.; YU, S. W.
- Abstract
We derive the formulas of the maximal and minimal ranks of four real matrices X 1, X2, X3 and X4 in common solution X = X1 + X2i + X3j + X4k to quaternion matrix equations A1X = C1, XB2 = C2, A3XB3 = C3. As applications, we establish necessary and sufficient conditions for the existence of the common real and complex solutions to the matrix equations. We give the expressions of such solutions to this system when the solvability conditions are met. Moreover, we present necessary and sufficient conditions for the existence of real and complex solutions to the system of quaternion matrix equations A1X = C1, XB2 = C2, A3 XB3 = C3, A4 XB4 = C4. The findings of this paper extend some known results in the literature.
- Subjects
MATHEMATICAL formulas; MATRICES (Mathematics); ALGEBRAIC equations; QUATERNIONS; COMPLEX numbers; UNIVERSAL algebra
- Publication
Bulletin of the Iranian Mathematical Society, 2012, Vol 38, Issue 1, p131
- ISSN
1018-6301
- Publication type
Article