{{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. Herm ...

(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, a parametrized family of discrete probability distributions * Hermite–Lindemann theorem, theorem about transcendental numbers * Hermite constant, a constant related to the geometry of certain lattices * Hermite-Gaussian modes * The Hermite–Hadamard inequality on convex functions and their integrals * Hermite interpolation, 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 numbers, 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 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 i ...

** Continuous q-Hermite polynomials **

Continuous big q-Hermite polynomials In mathematics, the continuous big ''q''-Hermite polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties. Definition The polynomials are given in terms of basic ...

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 ir ...

concerning covariants of binary forms * Hermite ring, a ring over which every stably free module is free of unique rank * Hermite-Sobolev spaces

Hermite's

* Hermite's cotangent identity, a trigonometric identity * Hermite's criterion * Hermite's identity, an identity on fractional parts of integer multiples of real numbers *

Hermite's problem Hermite's problem is an open problem in mathematics posed by Charles Hermite in 1848. He asked for a way of expressing real numbers as sequences of natural numbers, such that the sequence is eventually periodic precisely when the original number is ...

, an unsolved problem on certain ways of expressing real numbers *

Hermite's theorem In mathematics, the discriminant of an algebraic number field is a numerical invariant that, loosely speaking, measures the size of the (ring of integers of the) algebraic number field. More specifically, it is proportional to the squared volume ...

, 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 ...

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 ori ...

less than a given magnitude

Hermitian

* Einstein–Hermitian vector bundle **

Deformed Hermitian Yang–Mills equation In mathematics and theoretical physics, and especially gauge theory, the deformed Hermitian Yang–Mills (dHYM) equation is a differential equation describing the equations of motion for a D-brane in the B-model (commonly called a B-brane) of s ...

Hermitian adjoint In mathematics, specifically in operator theory, each linear operator A on a Euclidean vector space defines a Hermitian adjoint (or adjoint) operator A^* on that space according to the rule :\langle Ax,y \rangle = \langle x,A^*y \rangle, wher ...

Hermitian connection In mathematics, a Hermitian connection \nabla is a connection on a Hermitian vector bundle E over a smooth manifold M which is compatible with the Hermitian metric \langle \cdot, \cdot \rangle on E, meaning that : v \langle s,t\rangle = \langle \na ...

, 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 ...

, 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 In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the -t ...

, 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 it ...

'', an operator (sometimes a symmetric operator, sometimes a symmetric densely defined operator, sometimes a

self-adjoint 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 ...

) *

Hermitian 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 as i ...

, a classical orthogonal polynomial sequence that arise in probability *

Hermitian symmetric space In mathematics, a Hermitian symmetric space is a Hermitian manifold which at every point has an inversion symmetry preserving the Hermitian structure. First studied by Élie Cartan, they form a natural generalization of the notion of Riemannian ...

, 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, a generalisation of quadrics * Hermitian wavelet, a family of continuous wavelets * Non-Hermitian quantum mechanics

Astronomical objects

* 24998 Hermite, a

main-belt asteroid The asteroid belt is a torus-shaped region in the Solar System, located roughly between the orbits of the planets Jupiter and Mars. It contains a great many solid, irregularly shaped bodies, of many sizes, but much smaller than planets, cal ...

* Hermite (crater) Hermite