## An iterative method for the skew-symmetric solution and the optimal approximate solution of the matrix equation $$AXB=C$$.(English)Zbl 1146.65036

The authors introduce a simple algorithm to decide whether the matrix equation $$AXB=C$$ with compatibly dimensioned given matrices $$A, B$$, and $$C$$ has a skew-symmetric solution $$X$$. The algorithm finds this solution – if possible – in finitely many iterations for any given error bound. Moreover the same matrix equation for a modified right hand side $$\tilde C$$ and $$\tilde X$$ can be used to find the minimal norm skew-symmetric solution $$X$$ to the original $$AXB=C$$ equation. Both algorithms work for any skew-symmetric starting matrix.

### MSC:

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

### Keywords:

matrix equation; skew-symmetric solution; iterative method
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### References:

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