Echelon Form

 

Title: Echelon Form
Authors: Jose Divasón and Jesús Aransay
Submission date: 2015-02-12
Abstract: We formalize an algorithm to compute the Echelon Form of a matrix. We have proved its existence over Bézout domains and made it executable over Euclidean domains, such as the integer ring and the univariate polynomials over a field. This allows us to compute determinants, inverses and characteristic polynomials of matrices. The work is based on the HOL-Multivariate Analysis library, and on both the Gauss-Jordan and Cayley-Hamilton AFP entries. As a by-product, some algebraic structures have been implemented (principal ideal domains, Bézout domains...). The algorithm has been refined to immutable arrays and code can be generated to functional languages as well.
BibTeX:
@article{Echelon_Form-AFP,
  author  = {Jose Divasón and Jesús Aransay},
  title   = {Echelon Form},
  journal = {Archive of Formal Proofs},
  month   = feb,
  year    = 2015,
  note    = {\url{http://isa-afp.org/entries/Echelon_Form.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License
Depends on: Cayley_Hamilton, Gauss_Jordan
Used by: Hermite