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The Arithmetic Jacobian Matrix and Determinant
University of Tampere, Finland.
University of Tampere, Finland.
Tampere University of Technology, Finland.
Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.ORCID iD: 0000-0002-7494-4632
2017 (English)In: Journal of Integer Sequences, ISSN 1530-7638, E-ISSN 1530-7638, Vol. 20, no 9, article id 17.9.2Article in journal (Refereed) Published
Abstract [en]

Let a1,..., am be real numbers that can be expressed as a finite product of prime powers with rational exponents. Using arithmetic partial derivatives, we define the arithmetic Jacobian matrix Ja of the vector a = (a1,..., am) analogously to the Jacobian matrix Jf of a vector function f. We introduce the concept of multiplicative independence of {a1,..., am} and show that Ja plays in it a similar role as Jf does in functional independence. We also present a kind of arithmetic implicit function theorem and show that Ja applies to it somewhat analogously as Jf applies to the ordinary implicit function theorem.

Place, publisher, year, edition, pages
University of Waterloo , 2017. Vol. 20, no 9, article id 17.9.2
National Category
Discrete Mathematics Didactics
Research subject
Mathematics Education
Identifiers
URN: urn:nbn:se:ltu:diva-65566Scopus ID: 2-s2.0-85029696435OAI: oai:DiVA.org:ltu-65566DiVA, id: diva2:1140059
Note

Validerad;2017;Nivå 2;2017-09-12 (andbra)

Available from: 2017-09-11 Created: 2017-09-11 Last updated: 2017-11-24Bibliographically approved

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Scopushttps://cs.uwaterloo.ca/journals/JIS/VOL20/Tossavainen/tossa11.pdf

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Tossavainen, Timo

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CiteExportLink to record
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  • apa
  • harvard1
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