{{Short description, none Numerous things are named after the French mathematician

Charles Hermite Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra. Hermi ...

(1822–1901):

Hermite

* Cubic Hermite spline, a type of third-degree spline * Gauss–Hermite quadrature, an extension of Gaussian quadrature method *

Hermite class The Hermite or Pólya class is a set of entire functions satisfying the requirement that if ''E(z)'' is in the class, then:, E(x-iy), for positive ''y''. (However, a de Branges space can be defined using a function that is not in the class, such as ...

* Hermite differential equation *

Hermite distribution In probability theory and statistics, the Hermite distribution, named after Charles Hermite, is a discrete probability distribution used to model ''count data'' with more than one parameter. This distribution is flexible in terms of its ability to ...

, a parametrized family of discrete probability distributions * Hermite–Lindemann theorem, theorem about transcendental numbers *

Hermite constant In mathematics, the Hermite constant, named after Charles Hermite, determines how short an element of a lattice in Euclidean space can be. The constant ''γn'' for integers ''n'' > 0 is defined as follows. For a lattice ''L'' in Euclidean space ...

, a constant related to the geometry of certain lattices * Hermite-Gaussian modes * The

Hermite–Hadamard inequality In mathematics, the Hermite–Hadamard inequality, named after Charles Hermite and Jacques Hadamard and sometimes also called Hadamard's inequality, states that if a function ƒ : 'a'', ''b''nbsp;→ R is convex function, c ...

on convex functions and their integrals *

Hermite interpolation In numerical analysis, Hermite interpolation, named after Charles Hermite, is a method of polynomial interpolation, which generalizes Lagrange interpolation. Lagrange interpolation allows computing a polynomial of degree less than that takes the s ...

, a method of interpolating data points by a polynomial * Hermite–Kronecker–Brioschi characterization * The

Hermite–Minkowski theorem In mathematics, especially in algebraic number theory, the Hermite–Minkowski theorem states that for any integer ''N'' there are only finitely many number fields, i.e., finite field extensions ''K'' of the rational numbers Q, such that the di ...

, stating that only finitely many number fields have small discriminants * Hermite normal form, a form of row-reduced matrices *

Hermite number In mathematics, Hermite numbers are values of Hermite polynomials at zero argument. Typically they are defined for physicists' Hermite polynomials. Formal definition The numbers ''H''n = ''H''n(0), where ''H''n(''x'') is a Hermite polynomial of or ...

s, integers related to the Hermite polynomials *

Hermite polynomials In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: * signal processing as Hermitian wavelets for wavelet transform analysis * probability, such as the Edgeworth series, as well a ...

, a sequence of polynomials orthogonal with respect to the

normal distribution In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is : f(x) = \frac e^ The parameter \mu ...

** Continuous q-Hermite polynomials ** Continuous big q-Hermite polynomials **

Discrete q-Hermite polynomials In mathematics, the discrete ''q''-Hermite polynomials are two closely related families ''h'n''(''x'';''q'') and ''ĥ'n''(''x'';''q'') of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by . give a detai ...

** Wiener–Hermite expansion * Hermite reciprocity, a

reciprocity law In mathematics, a reciprocity law is a generalization of the law of quadratic reciprocity to arbitrary monic irreducible polynomials f(x) with integer coefficients. Recall that first reciprocity law, quadratic reciprocity, determines when an irr ...

concerning covariants of binary forms * Hermite ring, a

ring Ring may refer to: * Ring (jewellery), a round band, usually made of metal, worn as ornamental jewelry * To make a sound with a bell, and the sound made by a bell :(hence) to initiate a telephone connection Arts, entertainment and media Film and ...

over which every stably free module is free of unique rank * Hermite-Sobolev spaces

Hermite's

Hermite's cotangent identity In mathematics, Hermite's cotangent identity is a trigonometric identity discovered by Charles Hermite.Warren P. Johnson, "Trigonometric Identities à la Hermite", ''American Mathematical Monthly'', volume 117, number 4, April 2010, pages 311&nda ...

, a trigonometric identity * Hermite's criterion * Hermite's identity, an identity on fractional parts of integer multiples of real numbers * Hermite's problem, an unsolved problem on certain ways of expressing real numbers * Hermite's theorem, that there are only finitely many

algebraic number field In mathematics, an algebraic number field (or simply number field) is an extension field K of the field of rational numbers such that the field extension K / \mathbb has finite degree (and hence is an algebraic field extension). Thus K is a f ...

s of

discriminant In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them. More precisely, it is a polynomial function of the coefficients of the origi ...

less than a given magnitude

Hermitian

* Einstein–Hermitian vector bundle ** Deformed Hermitian Yang–Mills equation * Hermitian adjoint * Hermitian connection, the unique connection on a Hermitian manifold that satisfies specific conditions *

Hermitian form In mathematics, a sesquilinear form is a generalization of a bilinear form that, in turn, is a generalization of the concept of the dot product of Euclidean space. A bilinear form is linear in each of its arguments, but a sesquilinear form allows o ...

, a specific sesquilinear form * Hermitian function, a complex function whose complex conjugate is equal to the original function with the variable changed in sign * Hermitian manifold/structure ** Hermitian metric, is a smoothly varying positive-definite Hermitian form on each fiber of a complex vector bundle * Hermitian matrix, a square matrix with complex entries that is equal to its own conjugate transpose ** Skew-Hermitian matrix *''

Hermitian operator In mathematics, a self-adjoint operator on an infinite-dimensional complex vector space ''V'' with inner product \langle\cdot,\cdot\rangle (equivalently, a Hermitian operator in the finite-dimensional case) is a linear map ''A'' (from ''V'' to itse ...

'', an operator (sometimes a symmetric operator, sometimes a symmetric densely defined operator, sometimes a self-adjoint operator) * Hermitian polynomials, a classical orthogonal polynomial sequence that arise in probability * Hermitian symmetric space, a Kähler manifold which, as a Riemannian manifold, is a Riemannian symmetric space * Hermitian transpose, the transpose of a matrix and with the complex conjugate of each entry *

Hermitian variety In geometry, a unital is a set of ''n''3 + 1 points arranged into subsets of size ''n'' + 1 so that every pair of distinct points of the set are contained in exactly one subset. This is equivalent to saying that a unital is a 2-(''n''3 + 1, ''n'' ...

, a generalisation of quadrics * Hermitian wavelet, a family of continuous wavelets *

Non-Hermitian quantum mechanics PT symmetry was initially studied as a specific system in non-Hermitian quantum mechanics, where Hamiltonians are not Hermitian. In 1998, physicist Carl Bender and former graduate student Stefan Boettcher published in ''Physical Review Letters'' ...

Astronomical objects

* 24998 Hermite, a main-belt asteroid *

Hermite (crater) 240px, Lunar Orbiter 4 image of Hermite and surrounding craters Hermite is a lunar impact crater located along the northern lunar limb, close to the north pole of the Moon. Named for Charles Hermite, the crater was formed roughly 3.91 billion y ...

Hermite Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra. Hermi ...