Real representations of quaternion matrices and quaternion matrix equations. (Chinese. English summary) Zbl 1139.15300

Quaternion matrices and quaternion matrix equations play important roles in quantum mechanics. By introducing real representations of quaternion matrices, this paper studies the solution of the general quaternion matrix equation \(AXB-CYD= E\), and gives a practical technique of finding the solution of the quaternion matrix equation. This paper also obtains a Roth’s theorem over the quaternion field.


15A24 Matrix equations and identities
15B33 Matrices over special rings (quaternions, finite fields, etc.)
15A90 Applications of matrix theory to physics (MSC2000)