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UMINF 13.12

Symmetric matrix pencils: codimension counts and the solution of a pair of matrix equations

The set of all solutions to the homogeneous system of matrix equations (X^TA+AX,X^TB+BX)=(0,0), where (A,B) is a pair of symmetric matrices of the same size, is characterized. In addition, the codimension of the orbit of (A,B) under congruence is calculated. This paper is a natural continuation of the article [Linear Algebra Appl. 438:3375-3396, 2013] where the corresponding problems for skew-symmetric matrix pencils are solved. The new results will be useful in the development of the stratification theory for orbits of symmetric matrix pencils.


Pair of symmetric matrices; Matrix equations; Orbits; Codimension


Andrii Dmytryshyn , Bo Kågström and Vladimir V. Sergeichuk

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Entry responsible: Andrii Dmytryshyn

Page Responsible: Frank Drewes