Matrices as Arrows!

cting programs and point-free abstraction [2]. In order to automatically generate the fast running code there was the need to use matrix product as the basic matrix composition operator and matrices are viewed and transformed index-free. This matches the categorical characterization of matrices which can be traced back to [3] whereas each matrix is denoted as an arrow between its dimensions i.e. the natural numbers, objects of the category. R =    r11 . . . r1n ... ... ... rm1 . . . rmn    m×n m n Roo Because the Hom-Sets which are all matrices with the same dimensions form an additive group for which the composition is bilinear we are in the presence of an abelian category, property we found while trying to unveil how products and coproducts form in the category of matrices. What we found shook our computer scientist’s perspective about products/coproducts which we tend to use to capture heterogeneous concepts as tupling/alternative, conjunction/dijunction . . . [...

• Type: Conference
• Year: 2010
• Where: MPC
• Authors: Hugo Daniel Macedo, José Nuno Oliveira
• Keywords: Fast Running Code, Mathematics, Matrix Composition Operator, MPC 2010, Point-free Abstraction