State symmetries in matrices and vectors on finite state spaces

Details State symmetries in matrices and vectors on finite state spaces State symmetries in matrices and vectors on finite state spaces

2004-09-15

arxiv.org/abs/math/0409264v1

Mathematics

Rings and Algebras

35 pages, including a large number of examples

Scientific paper

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.

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