Given a diagonal anisotropic expanding matrix $D\in\ZZ^{\di\times\di},$ we show that it is always possible to detect a unimodular matrix $A\in\ZZ^{\di\times\di}$ that satisfies the pseudo-commuting properties \[DA=A^nD.\] In particular when $\di=2$ the more general relation \[DA^m=A^nD\] holds.
Bozzini, M., Ghisi, D., Rossini, M., Sauer, T. (2016). Directional transforms and pseudo-commuting properties. In Thirteenth international conference Zaragoza-Pau on mathematics and its applications. Monografías Matemáticas “García de Galdeano” (pp. 29-41). Prensas Univ. Zaragoza, Zaragoza.
Directional transforms and pseudo-commuting properties
ROSSINI, MILVIA FRANCESCA
;
2016
Abstract
Given a diagonal anisotropic expanding matrix $D\in\ZZ^{\di\times\di},$ we show that it is always possible to detect a unimodular matrix $A\in\ZZ^{\di\times\di}$ that satisfies the pseudo-commuting properties \[DA=A^nD.\] In particular when $\di=2$ the more general relation \[DA^m=A^nD\] holds.
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