Prove that for every skew-symmetric matrix A, there are symmetric matrices B and C such that A=BC-CB.
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Prove that for every skew-symmetric matrix A, there are symmetric matrices B and C such that A=BC-CB.
Let A, B be 2n×2n skew-symmetric matrices and let f be the characteristic polynomial of AB. Prove that the multiplicity of each root of f is at least 2.