• Corpus ID: 119730681

Orbits of the Centralizer of a Linear Operator

@article{Best2011OrbitsOT,
  title={Orbits of the Centralizer of a Linear Operator},
  author={PaulJ. Best and Marco Gualtieri and Patrick M. Hayden},
  journal={arXiv: Dynamical Systems},
  year={2011}
}
We describe the orbit structure for the action of the centralizer group of a linear operator on a finite-dimensional complex vector space. The main application is to the classification of solutions to a system of first-order ODEs with constant coefficients. We completely describe the lattice structure on the set of orbits and provide a generating function for the number of orbits in each dimension. 
2 Citations

Figures from this paper

NILPOTENT MODULES OVER POLYNOMIAL RINGS
Let $\mathbb K$ be an algebraically closed field of characteristic zero, $\mathbb K[X]$ the polynomial ring in $n$ variables. The vector space $T_n = \mathbb K[X]$ is a $\mathbb K[X]$-module with the
Nilpotent modules over polynomial rings
Let K be an algebraically closed field of characteristic zero, K[X ] the polynomial ring in n variables. The vector space Tn = K[X ] is a K[X ]-module with the action xi ·v = v ′ xi for v ∈ Tn. Every

References

SHOWING 1-3 OF 3 REFERENCES
What Is Enumerative Combinatorics
The basic problem of enumerative combinatorics is that of counting the number of elements of a finite set. Usually are given an infinite class of finite sets S i where i ranges over some index set I
Enumerative combinatorics, Vol. 1
  • Cambridge Studies in Advanced Mathematics
  • 1997