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 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...

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...

{\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}...

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

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...

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

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

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

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...

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

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...

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

_{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...

(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...

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...

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

Polynomial chaos (PC), also called polynomial chaos expansion (PCE) and Wiener chaos expansion, is a method for representing a random variable in terms...

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

Hilbert's fifth problem, and was a leader in reform and innovation in math­e­mat­ics teaching at all levels. Gleason's theorem in quantum logic and the...

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

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