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The matrix equation \(AXB-GXB=E\) over the quaternion field. (English) Zbl 0840.15017

Author’s abstract: Using the method of complex representation, this paper obtains necessary and sufficient conditions for the existence of a solution or a unique solution to the matrix equation \(AXB - GXD = E\) over the quaternion field, extends W. E. Roth’s theorem [Proc. Am. Math. Soc. 3, 392-396 (1952; Zbl 0047.01901)] and A. Jameson’s theorem [SIAM J. Appl. Math. 16, 1020-1023 (1968; Zbl 0169.35202)] to the quaternion field, and gives the representation of the solution.

MSC:

15B33 Matrices over special rings (quaternions, finite fields, etc.)
15A24 Matrix equations and identities
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References:

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