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.
Capitolo o saggio
Commuting property, integer matrix, shear matrix, directional transform
English
Thirteenth international conference Zaragoza-Pau on mathematics and its applications. Monografías Matemáticas “García de Galdeano”
2016
978-84-16515-68-4
40
Prensas Univ. Zaragoza, Zaragoza
29
41
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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/158084
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