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A pair of simultaneous linear matrix equations \(A_ 1XB_ 1=C_ 1,A_ 2XB_ 2=C_ 2\) and a matrix programming problem. (English) Zbl 0712.15010

This paper extends the author’s earlier result on solvability of a pair of simultaneous equations \(A_ 1\times B_ 1=C_ 1\) and \(A_ 2\times B_ 2=C_ 2\) on the complex field to a general field. Together with a set of necessary and sufficient conditions for the existence of a common solution, an expression for the general solution is provided.
Reviewer: M.E.Sezer

MSC:

15A24 Matrix equations and identities
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References:

[1] Khatri, C. G.; Mitra, S. K., Hermitian and nonnegative definite solutions of linear matrix equations, SIAM J. Appl. Math., 31, 579-585 (1976) · Zbl 0359.65033
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[3] Mitra, S. K., Common solutions to a pair of linear matrix equations \(A_1 XB_1 = C_1\) and \(A_2 XB_2 = C_2\), Proc. Cambridge Philos. Soc., 74, 213-216 (1973)
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