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State symmetries in matrices and vectors on finite state spaces

Arne Ring
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Abstract

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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Arne Ring. 2004-09-15. State symmetries in matrices and vectors on finite state spaces. https://arxiv.org/abs/math/0409264

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