# 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{https://isa-afp.org/entries/Echelon_Form.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Cayley_Hamilton, Gauss_Jordan, Rank_Nullity_Theorem Used by: Hermite