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...

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...

{\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...

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...

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...

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...

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...

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

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...

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...

(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...

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

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...

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...

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

and momentum the Hilbert space is the space of complex square-integrable functions L 2 ( C ) {\displaystyle L^{2}(\mathbb {C} )} , while the Hilbert space...

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

and some of its generalizations, along with Goldbach's conjecture and the twin prime conjecture, make up Hilbert's eighth problem in David Hilbert's list...

the denominator results in polynomial equations in the metric tensor and its first and second derivatives. The Einstein–Hilbert action from which the equations...