Gauss-Jordan Algorithm and Its Applications


Title: Gauss-Jordan Algorithm and Its Applications
Authors: Jose Divasón and Jesús Aransay
Submission date: 2014-09-03
Abstract: The Gauss-Jordan algorithm states that any matrix over a field can be transformed by means of elementary row operations to a matrix in reduced row echelon form. The formalization is based on the Rank Nullity Theorem entry of the AFP and on the HOL-Multivariate-Analysis session of Isabelle, where matrices are represented as functions over finite types. We have set up the code generator to make this representation executable. In order to improve the performance, a refinement to immutable arrays has been carried out. We have formalized some of the applications of the Gauss-Jordan algorithm. Thanks to this development, the following facts can be computed over matrices whose elements belong to a field: Ranks, Determinants, Inverses, Bases and dimensions and Solutions of systems of linear equations. Code can be exported to SML and Haskell.
  author  = {Jose Divasón and Jesús Aransay},
  title   = {Gauss-Jordan Algorithm and Its Applications},
  journal = {Archive of Formal Proofs},
  month   = sep,
  year    = 2014,
  note    = {\url{},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Depends on: Rank_Nullity_Theorem
Used by: Echelon_Form, Jordan_Normal_Form, QR_Decomposition