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]
^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.
^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)
^Adkins, William; Weintraub, Steven (2012-12-06). Algebra: An Approach via Module Theory. Springer Science & Business Media. p. 306. ISBN 9781461209232.
and 25 Related for: Hermite normal form information
friend M. Hermite well proposes to call them, their Canonical forms." In the same period, usage is attested by Hesse ("Normalform"), Hermite ("forme canonique")...
In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets...
b)M = (d 0), and the term left Hermite is defined similarly. Matrices over such a ring can be put in Hermitenormalform by right multiplication by a square...
a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of...
matrix used (possibly implicitly) in lattice reduction and in the Hermitenormalform of matrices. The Kronecker product of two unimodular matrices is...
1 ) − 5 / 4 {\displaystyle a=d_{0}(-d_{1})^{-5/4}} . This form is required by the Hermite–Kronecker–Brioschi method, Glasser's method, and the Cockle–Harley...
such as the reduction of the matrix of the system to Smith normalform or Hermitenormalform. However, as usual when using a general algorithm for a more...
{H}}} Hermitian matrices are named after Charles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices...
to linear Diophantine equations and abelian group with Hermitenormalform and Smith normalform. Before the 20th century, different types of eliminants...
reducing any kind of matrix format to a standard format called 'HermiteNormalform', which is a unit upper triangular matrix. Some of his other projects...
characteristic polynomial, eigenvalues (but not eigenvectors), Hermitenormalform, and Smith normalform.[citation needed] In his 1969 paper, where he proved the...
Head normalform Hednesford railway station, in England Heinz Nixdorf MuseumsForum, in Paderborn, Germany Hepatocyte nuclear factor Hermitenormalform Hesse...
In probability theory and statistics, the Hermite distribution, named after Charles Hermite, is a discrete probability distribution used to model count...
Bring–Jerrard normalform x5 − x + t = 0. The roots of this equation cannot be expressed by radicals. However, in 1858, Charles Hermite published the...
variable Z that is formed as the ratio Z = X/Y is a ratio distribution. An example is the Cauchy distribution (also called the normal ratio distribution)...
using Hermite functions. For unit variance, the n-th derivative of the Gaussian is the Gaussian function itself multiplied by the n-th Hermite polynomial...
algorithm on it and referring to the basis as B, matrix B is already in HermiteNormalForm so the first step is not needed. The determinant is d = 2 {\displaystyle...
and showed, in modernized notation, that it can be expanded in terms of Hermite polynomials H(.) based on weight function exp(−x²) as E ( x , y ) = ∑ n...
Global Information