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Zbl 1158.15010
Wang, Qing-Wen; Li, Cheng-Kun
Ranks and the least-norm of the general solution to a system of quaternion matrix equations.
(English)
[J] Linear Algebra Appl. 430, No. 5-6, 1626-1640 (2009). ISSN 0024-3795

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.
MSC 2000:
*15A24 Matrix equations
15A33 Matrices over special rings
15A09 Matrix inversion
15A03 Vector spaces

Keywords: system of quaternion matrix equations; minimal rank; maximal rank; Moore-Penrose inverse; least-norm; linear matrix expression

Citations: Zbl 1149.15011

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