Affine Independence in Vector Spaces

Karol Pąk
2010 Formalized Mathematics  
Affine Independence in Vector Spaces 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
more » ... prove selected properties of the barycentric coordinates.
doi:10.2478/v10037-010-0012-z fatcat:kldgpodazrbxjbaw3diwwc6zai