6,052 articles
Complex multiplication of abelian varieties
Complex multiplication of abelian varieties is the property that an abelian variety's endomorphism algebra is as large as possible, developed by Shimura and Taniyama and underlying class field theory.
Complex normal distribution
The complex normal distribution, also called the complex Gaussian distribution, describes complex-valued random variables and vectors whose real and imaginary parts are jointly Gaussian, with a mean and covariance.
Complex number
A complex number is a number x + iy, where x and y are real and i² = −1, completing the real numbers into an algebraically closed field.
Complex plane
The complex plane, also called the Argand plane, represents complex numbers as points, with the real part on the horizontal axis and the imaginary part on the vertical.
Complex projective space
Complex projective space, CP^n, is the space of complex lines through the origin in C^(n+1), a compact complex manifold that is a basic example in complex geometry and algebraic topology.
Complex question
The complex question, also called the fallacy of many questions (plurium interrogationum), is an informal fallacy where a question's wording presupposes an unestablished claim, so any direct answer concedes it.
Complex random variable
A complex random variable is a complex-valued function on a probability space, equivalent to a pair of real random variables, used to model signals in communication and signal processing.
Complex random vector
A complex random vector is a jointly distributed collection of complex-valued random variables, used to model baseband noise and signals in digital communications, radar, and array processing.
Complex structure
A complex structure on a real manifold is an atlas of charts with holomorphic transition maps, letting the manifold be treated locally as open sets in C^n.
Complex wavelet transform
The complex wavelet transform is a signal-processing method using complex-valued wavelets to gain phase information and approximate shift invariance over the standard discrete wavelet transform.
Complexity of numerical linear algebra
The complexity of numerical linear algebra counts the arithmetic operations needed for core matrix problems such as solving linear systems, least squares, inversion, and eigenvalue computation.
Composite endpoint
A composite endpoint is a single clinical trial outcome combining two or more events, such as cardiovascular death, stroke, or hospitalization, with occurrence of any one counting as the endpoint.
Composite number
A composite number, also called a factorable number, is a positive integer greater than 1 that is not prime, such as 6 = 2 × 3.
Composition algebra
A composition algebra is a not-necessarily-associative algebra with a nondegenerate quadratic form whose norm multiplies over products, with the real numbers, complex numbers, quaternions, and octonions as classical examples.
Composition series
A composition series of a group is a finite chain of subgroups, each normal in the next, whose simple quotients are its composition factors, unique by the Jordan–Hölder theorem.
Compositional data analysis
Compositional data analysis (CoDA) is the branch of statistics for data carrying only relative information, such as percentages and proportions, analyzing logratios within the simplex since Aitchison's 1986 monograph.
Compound Poisson process
A compound Poisson process is a stochastic process that stays constant between random jump times and jumps by independent random amounts, also called a continuous-time random walk.
Compound probability distribution
A compound probability distribution, also called a compound distribution, is the distribution of a sum of a random number of random variables, used to model insurance claims.
Compressed sensing
Compressed sensing (also called compressive sampling) is a signal acquisition technique, formalized around 2004, that recovers sparse signals from far fewer measurements than classical sampling theory requires.
Computability logic
Computability logic (CoL) is a formal theory of interactive computability introduced by logician Giorgi Japaridze in 2003, treating computational problems as games won by a machine.
Computable analysis
Computable analysis is the branch of mathematical logic and theoretical computer science that studies computability and complexity for real numbers, continuous functions, and differential equations.
Computable number
A computable number, also called a computable real, is a real number an algorithm can approximate to any precision, introduced by Alan Turing in 1936.
Computable set
A computable set, also called a recursive or decidable set, is a set of natural numbers whose membership an algorithm can always decide in finitely many steps.
Computably enumerable set
A computably enumerable set, also called a recursively enumerable set, is a set whose members can be listed by an algorithm, including non-computable sets like the halting problem.
Computation
Computation is the execution of an algorithm that transforms an input into an output by fixed rules, the foundation of computer science and, on some accounts, a physical process.
Computation for nonparametric Bayesian inference
Computation for nonparametric Bayesian inference covers the samplers and approximations, such as slice-based Gibbs and variational methods, used for infinite-dimensional priors like the Dirichlet process.
Computation tree logic
Computation tree logic (CTL) is a branching-time temporal logic used in formal verification, checked by model checking in linear time, and expressively incomparable with LTL.
Computational algebraic number theory
Computational algebraic number theory is the study of algorithms for computing with algebraic number fields, framed by Hendrik Lenstra's 1992 survey around Galois groups, rings of integers, and class groups.
Computational complexity of matrix multiplication
The computational complexity of matrix multiplication is measured by the exponent ω: Strassen's 1969 algorithm gave ω < 2.81, and the best bound is now ω < 2.371177.
Computational complexity theory
Computational complexity theory, or complexity theory in computation, classifies computational problems by the resources, such as time and memory, needed to solve them, and studies the P versus NP problem.