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UMINF 12.05

The solution of a pair of matrix equations (X^T A+A X, X^T B+B X)=(0, 0) with skew-symmetric A and B

The homogeneous system of matrix equations (X^T A+A X, X^T B+B X)=(0, 0), where (A, B) is a pair of skew-symmetric matrices of the same size is considered: we establish the general solution and calculate the codimension of the orbit of (A, B) under congruence.

Keywords

Pair of skew-symmetric matrices; Matrix equations; Orbits; Codimension

Authors

Andrii Dmytryshyn , Bo Kågström and Vladimir Sergeichuk

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Entry responsible: Andrii Dmytryshyn

Page Responsible: Frank Drewes
2022-09-30