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Ranks and the least-norm of the general solution to a system of quaternion matrix equations. (English) Zbl 1158.15010
The authors consider the system of linear quaternion matrix equations $A_1X_1=C_1$, $A_2X_2=C_2$, $A_3X_1B_1+A_4X_2B_2=C_3$ which is presumed consistent. They establish a new expression of its general solution; the system has been investigated recently by {\it Q.-W. Wang, H.-X. Chang} and {\it C.-Y. Lin} [Appl. Math. Comput. 195, No. 2, 721--732 (2008; Zbl 1149.15011)]. The authors derive the minimal and maximal ranks and the least-norm of the general solution to the system. Some previously known results are special cases of the ones in this paper.

15A24Matrix equations and identities
15B33Matrices over special rings (quaternions, finite fields, etc.)
15A09Matrix inversion, generalized inverses
15A03Vector spaces, linear dependence, rank
Full Text: DOI
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