Hermite normal form

In linear algebra, the Hermite normal form is an analogue of reduced echelon form for matrices over the integers Z. Just as reduced echelon form can be used to solve problems about the solution to the linear system Ax=b where x is in Rn, the Hermite normal form can solve problems about the solution to the linear system Ax=b where this time x is restricted to have integer coordinates only. Other applications of the Hermite normal form include integer programming,[1] cryptography,[2] and abstract algebra.[3]

  1. ^ Hung, Ming S.; Rom, Walter O. (1990-10-15). "An application of the Hermite normal form in integer programming". Linear Algebra and Its Applications. 140: 163–179. doi:10.1016/0024-3795(90)90228-5.
  2. ^ Evangelos, Tourloupis, Vasilios (2013-01-01). "Hermite normal forms and its cryptographic applications". University of Wollongong Thesis Collection 1954-2016. University of Wollongong.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  3. ^ Adkins, William; Weintraub, Steven (2012-12-06). Algebra: An Approach via Module Theory. Springer Science & Business Media. p. 306. ISBN 9781461209232.