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The nearest bisymmetric solutions of linear matrix equations. (English) Zbl 1068.65057

Necessary and sufficient conditions for the existence of bisymmetric solutions as well as expressions for such solutions are derived for the equations
(1) \(A_1X_1B_1+\cdots +A_kX_kB+k= D\),
(2) \(A_1\times B_1+\cdots+ A_k\times B_k= D\) and
(3) \((A_1\times B_1,\dots, A_k\times B_k)= (D_1,\dots, D_k)\).
They are based on Kronecker products and Moore-Penrose generalized inverses. The closest solution of these equations to a given matrix in the Frobenius norm is also provided. Numerical examples illustrate the methodology.

MSC:

65F30 Other matrix algorithms (MSC2010)
15A24 Matrix equations and identities
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