6,052 articles
Higher-order function
A higher-order function is a function that takes one or more functions as arguments, returns a function as its result, or both, as in map, filter, and fold.
Higher-order logic
Higher-order logic (HOL), also called simple type theory or Church's type theory, extends first-order logic by quantifying over predicates and functions via the simply typed lambda calculus; standard semantics is not axiomatizable, Henkin semantics is complete, and HOL underlies proof assistants like Isabelle/HOL and HOL Light.
Higher-order singular value decomposition
The higher-order singular value decomposition (HOSVD), also known as higher-order SVD, is a multilinear generalization of the matrix SVD, introduced by De Lathauwer, De Moor, and Vandewalle in 2000.
Highest-weight theory
Highest-weight theory is the branch of representation theory classifying representations of semisimple Lie algebras and Lie groups by a single linear functional, the highest weight, attached to each irreducible representation.
Highly accelerated life test
A highly accelerated life test (HALT) is a qualitative reliability engineering method that stresses electronics with extreme temperatures and vibration to expose design weaknesses, without predicting product life.
Highly composite number
A highly composite number, also called an anti-prime or maximally divisible number, is a positive integer with more divisors than any smaller one, first analyzed by Ramanujan in 1915.
Hilbert C*-module
A Hilbert C-module is a right module over a C-algebra with an algebra-valued inner product, generalizing Hilbert spaces and central to KK-theory and noncommutative geometry.
Hilbert class field
The Hilbert class field of a number field K is its unique maximal unramified abelian extension, with Galois group isomorphic to K's ideal class group.
Hilbert cube
The Hilbert cube is the compact subset of the Hilbert space l₂ whose coordinates are bounded by (1/2)ⁿ, a standard model space in infinite-dimensional topology.
Hilbert curve
The Hilbert curve is a continuous, nowhere differentiable space-filling fractal curve described by David Hilbert in 1891, whose locality makes it a standard tool for indexing multidimensional data in databases and geospatial systems.
Hilbert matrix
The Hilbert matrix is the square matrix with entries 1/(i + j − 1), the standard example of a badly ill-conditioned matrix in numerical linear algebra.
Hilbert scheme
The Hilbert scheme is a fundamental parameter space in algebraic geometry that parametrizes fixed closed sub-schemes of a scheme or projective space having a fixed Hilbert polynomial.
Hilbert space
A Hilbert space is a complete vector space with an inner product, formulated from David Hilbert's work on integral equations and central to quantum mechanics and signal processing.
Hilbert symbol
The Hilbert symbol, also called the norm residue symbol, is a pairing on a local field that tests whether an element is a norm, central to reciprocity laws.
Hilbert system
The Hilbert system, also called the Hilbert calculus, is a formal proof system for logic with many axiom schemas and few rules, usually just modus ponens.
Hilbert transform
The Hilbert transform is a linear integral operator, named for David Hilbert, that shifts each frequency component of a signal in phase by 90 degrees.
Hilbert–Bernays provability conditions
The Hilbert–Bernays provability conditions, given by Hilbert and Bernays in Grundlagen der Mathematik (1939), are conditions on a formalized provability predicate sufficient for proving Gödel's second incompleteness theorem.
Hilbert–Pólya conjecture
The Hilbert–Pólya conjecture in number theory proposes that the Riemann zeta function's non-trivial zeros are eigenvalues of a self-adjoint operator, which would prove the Riemann hypothesis.
Hilbert's axioms
Hilbert's axioms, also called Hilbert's axiom system, are a rigorous axiomatization of Euclidean geometry presented by David Hilbert in his 1899 monograph Grundlagen der Geometrie.
Hilbert's basis theorem
Hilbert's basis theorem is a theorem of David Hilbert, proved in 1890, stating that if a ring R is Noetherian, then the polynomial ring R[x] is also Noetherian.
Hilbert's fifth problem
Hilbert's fifth problem, posed by David Hilbert in 1900, asks whether every locally Euclidean topological group is a Lie group, answered affirmatively in 1952 by Gleason, Montgomery, and Zippin.
Hilbert's Nullstellensatz
Hilbert's Nullstellensatz, German for "zero locus theorem," is David Hilbert's 1893 theorem bridging commutative algebra and algebraic geometry: over an algebraically closed field, ideals of polynomials correspond precisely to the sets of their common zeros.
Hilbert's paradox of the Grand Hotel
Hilbert's paradox of the Grand Hotel, also known as Hilbert's Hotel, is a thought experiment in which a fully occupied infinite hotel still makes room for new guests.
Hilbert's problems
Hilbert's problems, also listed as the List of Hilbert's problems, are 23 mathematical problems David Hilbert presented at the 1900 Paris congress; several, including the Riemann Hypothesis, remain unsolved.
Hilbert's program
Hilbert's program was David Hilbert's 1920s proposal to secure mathematics by proving formal axiomatic systems consistent using finitary methods; Gödel's incompleteness theorems showed it could not succeed.
Hilbert's sixth problem
Hilbert's sixth problem is one of the 23 problems David Hilbert posed at the International Congress of Mathematicians in Paris in 1900, asking that mathematics axiomatize probability and mechanics.
Hilbert's tenth problem
Hilbert's tenth problem is the 1900 challenge of finding an algorithm that decides whether any Diophantine equation has integer solutions; Matiyasevich proved in 1970 that none exists.
Hilbert's Theorem 90
Hilbert's Theorem 90 is an algebra theorem stating that for a finite cyclic field extension, every norm-one element is a quotient y/σ(y), proved as Satz 90 of Hilbert's 1897 Zahlbericht.
Hilbert's twelfth problem
Hilbert's twelfth problem, also known as Kronecker's Jugendtraum, was posed by David Hilbert in 1900 and asks for explicit constructions of all abelian extensions of a number field.
Hill cipher
The Hill cipher is a classical polygraphic cipher invented by Lester S. Hill in 1929 that encrypts blocks of letters using an invertible key matrix modulo 26.