In commutative algebra, the Hilbert function, the Hilbert polynomial, and the Hilbert series of a graded commutative algebra finitely generated over a...

Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several...

In mathematics, a Hilbert space is a real or complex inner product space that is also a complete metric space with respect to the metric induced by the...

Hilbert ring Hilbert–Poincaré series Hilbert series and Hilbert polynomial Hilbert space Hilbert spectrum Hilbert system Hilbert transform Hilbert's arithmetic...

the Hilbert polynomial in cases when the latter exists; however, the Hilbert–Poincaré series describes the rank in every degree, while the Hilbert polynomial...

negative or zero: 0, ±1, ±2, ... . So Hilbert was asking for a general algorithm to decide whether a given polynomial Diophantine equation with integer coefficients...

term Hilbert dimension may refer to: Hilbert space dimension Hilbert dimension in ring theory, see Hilbert's basis theorem Hilbert series and Hilbert polynomial...

arises in the least squares approximation of arbitrary functions by polynomials. The Hilbert matrices are canonical examples of ill-conditioned matrices, being...

{\displaystyle f} in I {\displaystyle I} . Hilbert's Nullstellensatz states that if p is some polynomial in k [ X 1 , … , X n ] {\displaystyle k[X_{1}...

variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials. The basic theory of Hilbert schemes was...

Hilbert's eleventh problem is one of David Hilbert's list of open mathematical problems posed at the Second International Congress of Mathematicians in...

In mathematics, Riemann–Hilbert problems, named after Bernhard Riemann and David Hilbert, are a class of problems that arise in the study of differential...

x_{n}).} Multi-homogeneous polynomial Quasi-homogeneous polynomial Diagonal form Graded algebra Hilbert series and Hilbert polynomial Multilinear form Multilinear...

mathematics, Hilbert's syzygy theorem is one of the three fundamental theorems about polynomial rings over fields, first proved by David Hilbert in 1890,...

sum of squares of other polynomials. In 1888, Hilbert showed that every non-negative homogeneous polynomial in n variables and degree 2d can be represented...

_{I}(M))} , often called the Hilbert-Samuel polynomial (or Hilbert polynomial). For the ring of formal power series in two variables k [ [ x , y ] ] {\displaystyle...

kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional. Specifically, a Hilbert space...

of Bézout's theorem. (For a proof, see Hilbert series and Hilbert polynomial § Degree of a projective variety and Bézout's theorem.) The degree is not an...

order polynomial solutions to the Sturm–Liouville equations in the setting of Hilbert space. These include the Legendre and Laguerre polynomials as well...

abbreviated P(x, y) = 0) where P(x, y) is a polynomial with integer coefficients, where x1, ..., xj indicate parameters and y1, ..., yk indicate unknowns. A Diophantine...

(sketched) proof using Hilbert series, see Hilbert series and Hilbert polynomial § Degree of a projective variety and Bézout's theorem. Beside allowing a conceptually...

Hilbert number Hilbert plane Hilbert polynomial Hilbert series Hilbert ring Hilbert–Samuel function Hilbert projection theorem Hilbert R-tree Hilbert...

Classically, the theory dealt with the question of explicit description of polynomial functions that do not change, or are invariant, under the transformations...

challenge posed by David Hilbert and Wilhelm Ackermann in 1928. It asks for an algorithm that considers an inputted statement and answers "yes" or "no" according...

generalization of the law of quadratic reciprocity to arbitrary monic irreducible polynomials f ( x ) {\displaystyle f(x)} with integer coefficients. Recall that first...

numerical polynomials.[citation needed] The K-theory of BU(n) is numerical (symmetric) polynomials. The Hilbert polynomial of a polynomial ring in k + 1...

numerical analysis and mathematical analysis, a trigonometric polynomial is a finite linear combination of functions sin(nx) and cos(nx) with n taking...

mathematical logic and in the philosophy of mathematics. The theorems are interpreted as showing that Hilbert's program to find a complete and consistent set...

In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets...

curves (and higher-dimensional varieties). One of the important consequences of Riemann–Roch is it gives a formula for computing the Hilbert polynomial of...