# Affine Independence in Vector Spaces

Formalized Mathematics (2010)

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

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topKarol 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 -

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