@MISC{RLAFFIN1.MIZ,
  AUTHOR = {P\c{a}k, Karol},
  TITLE = {Affine Indepedence in Vector Spaces},
  SECTION1 = {Preliminaries},
  SECTION2 = {Two Transformations of Linear Combinations},
  SECTION3 = {The Sum of Coefficients of a Linear Combination},
  SECTION4 = {Affine Independence of Vectors},
  SECTION5 = {Affine Hull},
  SECTION6 = {Barycentric Coordinates},
  DAY = {18},
  MONTH = {December},
  YEAR = {2009},
  ADDRESS1 = {University of Bialystok, ul. Akademicka 2, 15-267 Bialystok},
  SUMMARY = {In this article we describe the notion of affinely
  indepedent subset of a real linear space. First we prove selected
  theorems concerning operations on linear combinations. Then we
  introduce affine indepedence 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.}}
