{{Short description, none Numerous things are named after the French mathematician Charles Hermite (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, 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, 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 ...

, 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 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, 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, 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 ...

, 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 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, 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 * Hermite (crater) Hermite