The solution of the equation XA + AXT = 0 and its application to the theory of orbits

@article{Tern2011TheSO,
  title={The solution of the equation XA + AXT = 0 and its application to the theory of orbits},
  author={F. Ter{\'a}n and F. M. Dopico},
  journal={Linear Algebra and its Applications},
  year={2011},
  volume={434},
  pages={44-67}
}
Abstract describe how to find the general solution of the matrix equation XA + AX T = 0 , with A ∈ C n × n , which allows us to determine the dimension of its solution space. This result has immediate applications in the theory of congruence orbits of matrices in C n × n , because the set { XA + AX T : X ∈ C n × n } is the tangent space at A to the congruence orbit of A. Hence, the codimension of this orbit is precisely the dimension of the solution space of XA + AX T = 0 . As a consequence, we… Expand
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References

SHOWING 1-10 OF 30 REFERENCES
CLASSIFICATION PROBLEMS FOR SYSTEMS OF FORMS AND LINEAR MAPPINGS
Canonical matrices of bilinear and sesquilinear forms
The Equations ATX\pm XTA=B
  • H. Braden
  • Mathematics, Computer Science
  • SIAM J. Matrix Anal. Appl.
  • 1998
The dimension of matrices (matrix pencils) with given Jordan (Kronecker) canonical forms
Congruences of a square matrix and its transpose
A Note on Generic Kronecker Orbits of Matrix Pencils with Fixed Rank
The Theory of Matrices
...
1
2
3
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