State symmetries in matrices and vectors on finite state spaces
- Resource Type
- Working Paper
- Authors
- Ring, Arne
- Source
- Subject
- Mathematics - Rings and Algebras
05E20
15A03
20G20
- Language
State symmetries are defined as permutations which act on vector spaces of column vectors and square matrices, resulting in isotropy groups for specific vector spaces. A large number of properties for such objects is shown, to provide a rigorous basis for future applications. The main statement characterises the state symmetry of vector sequences $(v^{(i)})$ which are generated by powers of a generator matrix $M$: $v^{(i)}= M^i v^{(0)}$. A section of examples illustrates some applications of the theory.
Comment: 35 pages, including a large number of examples