A soft introduction to algebraic entropy
type: Item
instance of: scholarly article
title: A soft introduction to algebraic entropy
zbMATH Open document ID: 1282.15006
author: Anna Giordano Bruno
author: Luigi Salce
published in: Arabian Journal of Mathematics
publication date: 2012-12-18T00:00:00Z
review text: The notion of algebraic entropy of a linear transformation \(\Phi\) on a vector space \(V\) over a field \(K\) is introduced and its basic properties are proved. The definition is given as the supremum on finite dimensional subspaces \(F\) of \(V\) by \(\lim _{n} \dim (F+\Phi F+\dots+\Phi ^{n-1}F)/n\). A characterization of linear transformations with finite algebraic entropy is given. The paper finishes analyzing the notion of adjoint algebraic entropy, also defined by means of dimensions of preimages of subspaces of \(V\) with finite codimension. The adjoint algebraic entropy is proved to be either 0 or infinite.
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 37B99
Mathematics Subject Classification ID: 37A35
zbMATH DE Number: 6116566
zbMATH Keywords: algebraic entropy
zbMATH Keywords: linear transformations
zbMATH Keywords: adjoint algebraic entropy
reviewed by: Jose S. Canovas
MaRDI profile type: Publication
full work available at URL: s40065-012-0024-3
OpenAlex ID: W2002293910
Wikidata QID: Q59270823
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DOI: 10.1007/S40065-012-0024-3
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description: scientific article; zbMATH DE number 6116566