## Least-norm of the general solution to some system of quaternion matrix equations and its determinantal representations.(English)Zbl 1457.15017

Summary: We constitute some necessary and sufficient conditions for the system $$A_1 X_1 = C_1$$, $$X_1 B_1 = C_2$$, $$A_2 X_2 = C_3$$, $$X_2 B_2 = C_4$$, $$A_3 X_1 B_3 + A_4 X_2 B_4 = C_c$$, to have a solution over the quaternion skew field in this paper. A novel expression of general solution to this system is also established when it has a solution. The least norm of the solution to this system is also researched in this article. Some former consequences can be regarded as particular cases of this article. Finally, we give determinantal representations (analogs of Cramer’s rule) of the least norm solution to the system using row-column noncommutative determinants. An algorithm and numerical examples are given to elaborate our results.

### MSC:

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

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