Fractions, Projective Representation, Duality, Linear Algebra and Geometry

Abstract: This contribution describes relationship between fractions, projective representation, duality, linear algebra and geometry. Many problems lead to a system of linear equations. This paper presents equivalence of the Cross-product operation and solution of a system of linear equations Ax=0 or Ax=b using projective space representation and homogeneous coordinates. It leads to conclusion that division operation is not required for a solution of a system of linear equations, if the projective representation and homogeneous coordinates are used. An efficient solution on CPU and GPU based architectures is presented with an application to barycentric coordinates computation as well.