Affine Independence in Vector Spaces

• Autorzy: Karol Pąk
• Języki publikacji: EN

Abstrakty

EN

In this article we describe the notion of affinely independent subset of a real linear space. First we prove selected theorems concerning operations on linear combinations. Then we introduce affine independence and prove the equivalence of various definitions of this notion. We also introduce the notion of the affine hull, i.e. a subset generated by a set of vectors which is an intersection of all affine sets including the given set. Finally, we introduce and prove selected properties of the barycentric coordinates.

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2010
• Tom: 18
• Numer: 1
• Strony: 87-93

Daty

wydano

2010-01-01

online

2011-01-05

Twórcy

autor

Karol Pąk

• Institute of Informatics, University of Białystok, Poland

Bibliografia

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Identyfikatory

DOI

10.2478/v10037-010-0012-z