Affine Independence in Vector Spaces

Karol Pąk

Formalized Mathematics (2010)

  • Volume: 18, Issue: 1, page 87-93
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Karol Pąk. "Affine Independence in Vector Spaces." Formalized Mathematics 18.1 (2010): 87-93. <http://eudml.org/doc/267401>.

@article{KarolPąk2010,
abstract = {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.},
author = {Karol Pąk},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {87-93},
title = {Affine Independence in Vector Spaces},
url = {http://eudml.org/doc/267401},
volume = {18},
year = {2010},
}

TY - JOUR
AU - Karol Pąk
TI - Affine Independence in Vector Spaces
JO - Formalized Mathematics
PY - 2010
VL - 18
IS - 1
SP - 87
EP - 93
AB - 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.
LA - eng
UR - http://eudml.org/doc/267401
ER -

References

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