{{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. Hermite p ...

(1822–1901):

Hermite

Cubic Hermite spline In numerical analysis, a cubic Hermite spline or cubic Hermite interpolator is a spline where each piece is a third-degree polynomial specified in Hermite form, that is, by its values and first derivatives at the end points of the correspondin ...

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

Gaussian quadrature In numerical analysis, an -point Gaussian quadrature rule, named after Carl Friedrich Gauss, is a quadrature rule constructed to yield an exact result for polynomials of degree or less by a suitable choice of the nodes and weights for . Th ...

method * Hermite class * 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 t ...

, 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 long a shortest 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 Euclidea ...

, a constant related to the geometry of certain lattices * Hermite-Gaussian modes * The Hermite–Hadamard inequality 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 th ...

, 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 discri ...

, stating that only finitely many number fields have small discriminants *

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 \in \mathbb^n, the ...

, 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 ...

, a sequence of polynomials orthogonal with respect to the

normal distribution In probability theory and 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 ...

** Continuous q-Hermite polynomials ** Continuous big q-Hermite polynomials ** Discrete q-Hermite polynomials ** 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 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. Hermite p ...

, a

ring (The) Ring(s) 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 Arts, entertainment, and media Film and TV * ''The Ring'' (franchise), a ...

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 In mathematics, Hermite's identity, named after Charles Hermite, gives the value of a summation involving the floor function. It states that for every real number ''x'' and for every positive integer ''n'' the following identity holds:. : \sum_ ...

, 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 ...

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 zero of a function, roots without computing them. More precisely, it is a polynomial function of the coef ...

less than a given magnitude

Hermitian

* Einstein–Hermitian vector bundle ** Deformed Hermitian Yang–Mills equation *

Hermitian adjoint In mathematics, specifically in operator theory, each linear operator A on an inner product 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, where \l ...

* 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 map, linear in each of its arguments, but a sesquilinear f ...

, a specific sesquilinear form *

Hermitian function In mathematical analysis, a Hermitian function is a complex function with the property that its complex conjugate is equal to the original function with the variable changed in sign: :f^*(x) = f(-x) (where the ^* indicates the complex conjugate) ...

, a complex function whose complex conjugate is equal to the original function with the variable changed in sign *

Hermitian manifold In mathematics, and more specifically in differential geometry, a Hermitian manifold is the complex analogue of a Riemannian manifold. More precisely, a Hermitian manifold is a complex manifold with a smoothly varying Hermitian inner product on ea ...

/structure **

Hermitian metric In mathematics, and more specifically in differential geometry, a Hermitian manifold is the complex analogue of a Riemannian manifold In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as ...

, 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 ...

, a square matrix with complex entries that is equal to its own conjugate transpose **

Skew-Hermitian matrix __NOTOC__ In linear algebra, a square matrix with complex entries is said to be skew-Hermitian or anti-Hermitian if its conjugate transpose is the negative of the original matrix. That is, the matrix A is skew-Hermitian if it satisfies the relation ...

*''

Hermitian operator In mathematics, a self-adjoint operator on a complex vector space ''V'' with inner product \langle\cdot,\cdot\rangle is a linear map ''A'' (from ''V'' to itself) that is its own adjoint. That is, \langle Ax,y \rangle = \langle x,Ay \rangle for al ...

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

self-adjoint operator In mathematics, a self-adjoint operator on a complex vector space ''V'' with inner product \langle\cdot,\cdot\rangle is a linear map ''A'' (from ''V'' to itself) that is its own adjoint. That is, \langle Ax,y \rangle = \langle x,Ay \rangle for al ...

) * Hermitian polynomials, 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 In mathematics, the conjugate transpose, also known as the Hermitian transpose, of an m \times n complex matrix \mathbf is an n \times m matrix obtained by transposing \mathbf and applying complex conjugation to each entry (the complex conjugate ...

, the transpose of a matrix and with the complex conjugate of each entry * Hermitian variety, a generalisation of quadrics *

Hermitian wavelet Hermitian wavelets are a family of discrete and continuous wavelets used in the constant and discrete Hermite wavelet transforms. The n^\textrm Hermitian wavelet is defined as the normalized n^\textrm derivative of a Gaussian distribution for ea ...

, 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, centered on the Sun and roughly spanning the space between the orbits of the planets Jupiter and Mars. It contains a great many solid, irregularly shaped bodies called asteroids ...

* Hermite (crater)

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. Hermite p ...