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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 Q.-W. Wang, H.-X. Chang and 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:

15A24 Matrix equations and identities
15B33 Matrices over special rings (quaternions, finite fields, etc.)
15A09 Theory of matrix inversion and generalized inverses
15A03 Vector spaces, linear dependence, rank, lineability

Citations:

Zbl 1149.15011
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Full Text: DOI

References:

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