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The least square solution with the least norm to a system of quaternion matrix equations. (English) Zbl 1397.15011

Summary: We in this paper derive the expression of the least square solution with the least norm to the system of generalized Sylvester quaternion matrix equations \[ \begin{aligned} A_1X=E_1,\quad XB_1=E_2,\quad C_1Y=E_3,\quad YD_1=E_4,\quad A_2XB_2+C_2YD_2=E_5, \end{aligned} \] where \(X\), \(Y\) are unknown quaternion matrices and the others are given quaternion matrices.

MSC:

15A24 Matrix equations and identities
15A06 Linear equations (linear algebraic aspects)
15A09 Theory of matrix inversion and generalized inverses
15B33 Matrices over special rings (quaternions, finite fields, etc.)
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