Abstract

Let F R C H , , . Let Un n be the set of unitary bimatrics in , F n n and let On n be the set of orthogonal bimatrices in . F n n Suppose n 2. we show that every A F B n n can be written as a sum of bimatrices in Un n and of bimatrices in . On n let A F B n n be given that and let k 2 be the least integer that is a least upper bound of the singular values of AB. When F=R, we show that if k 3, then AB can be written as a sum of 6 orthogonal bimatrices; if k 4, we show that AB can be written as a sum of k 2 orthogonal bimatrices.

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References

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