Degree growth of matrix inversion: birational maps of symmetric, cyclic matrices

Abstract

We consider two (densely defined) involutions on the space of $q\times q$ matrices; $I(x_{ij})$ is the matrix inverse of $(x_{ij})$, and $J(x_{ij})$ is the matrix whose $ij$th entry is the reciprocal $x_{ij}^{-1}$. Let $K=I\circ J$. The set ${\mathcal{SC}}_q$ of symmetric, cyclic matrices is invariant under $K$. In this paper, we determine the degrees of the iterates $K^n=K\circ ...\circ K$ restricted to ${\mathcal{SC}}_q$.

References in corpus (2)

• On the complexity of some birational transformations
• Periodicities in Linear Fractional Recurrences: Degree growth of birational surface maps

Cited by in corpus (1)

• Linear Recurrences in the Degree Sequences of Monomial Mappings