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

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

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

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

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...

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...

{\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}...

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

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...

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

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

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...

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...

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

_{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...

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

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

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

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...

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

or more variables. In 1890, David Hilbert proved a similar statement for the invariants of homogeneous polynomials in any number of variables. Furthermore...

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

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

or mixed states in a Hilbert space; the transition function is replaced by a collection of unitary matrices that map the Hilbert space to itself. That...

In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the...

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...

set of dimension d. The degree of the Hilbert polynomial of A. The degree of the denominator of the Hilbert series of A. This allows, through a Gröbner...