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Suppose that the matrix equations system .A 1 XB 1 ; : : : ; A k XB k / D .C 1 ; : : : ; C k / with unknown matrix X is given, where A i , B i , and C i , i D 1; 2; : : : ; k; are known matrices of suitable sizes. The matrix nearness problem is considered over the general and least squares solutions of this system. The explicit forms of the best approximate solutions of the problems over the sets of symmetric and skew-symmetric matrices are established as well. Moreover, a comparative table depending on some numerical examples in the literature is given.

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A remark stated in the end of the second section of the paper is not true since the matrices X − 1 2 X 0 + V X 0 V and 1 2 X 0 − V X 0 V (or the matrices X − 1 2 X 0 − V X 0 V and 1 2 X 0 + V X 0 V ) are not, in general, orthogonal. However, this remark was not used to derive results in the paper. Consequently, the remark, which is copied below, should be ignored."The minimization problem min X − X 0 is equivalent to the minimization problemover the set of H m,n since The online version of the original article can be found under