6,052 articles
Characteristic function (probability theory)
In probability theory, the characteristic function of a random variable is the Fourier transform φ(t) = E[e^{itX}], which always exists and uniquely determines the distribution.
Characteristic polynomial
The characteristic polynomial of a square matrix is the determinant of the matrix minus a scalar variable λ, and its roots are the matrix's eigenvalues.
Characteristic set
A characteristic set is a minimal triangular system of polynomials for a polynomial or differential ideal, introduced by Ritt in 1932 and reshaped by Wu Wen-tsün in the late 1970s.
Chart
A chart is a graphical representation of data in which values are encoded as bars, lines, points, or sectors, letting readers grasp patterns, comparisons, and trends at a glance.
Chebyshev approximation
Chebyshev approximation, also called minimax or uniform approximation, finds the polynomial minimizing a function's maximum error on an interval; it is computed by the Remez algorithm.
Chebyshev function
The Chebyshev functions are two number-theory functions, θ(x) and ψ(x), that weigh primes and prime powers by the logarithm of the prime; ψ(x) ~ x is equivalent to the prime number theorem.
Chebyshev nodes
Chebyshev nodes, or Chebyshev points, are interpolation sample points given by zeros or extrema of Chebyshev polynomials; clustered near interval endpoints, they avoid Runge divergence.
Chebyshev polynomials
Chebyshev polynomials, also called Tchebycheff polynomials, are orthogonal polynomials on −1 to 1 introduced by Pafnuty Chebyshev in 1854, used in approximation, spectral methods, and quantum algorithms.
Chebyshev's inequality
Chebyshev's inequality, also called the Bienaymé-Chebyshev inequality, is a theorem of probability theory stating that a random variable lies more than ε from its mean with probability at most Var(X)/ε².
Chemical graph theory
Chemical graph theory is the branch of graph theory that represents molecules as graphs, with atoms as vertices and bonds as edges, analyzed with topological indices.
Chemical reaction network
A chemical reaction network (CRN) is a mathematical model representing a chemical system as species, reactions, and rate constants, applied in systems biology and molecular computing.
Chern class
Chern classes are characteristic classes assigned to complex vector bundles, cohomology classes introduced by Shiing-Shen Chern in 1946 that measure how a bundle is globally twisted.
Chern–Simons theory
Chern–Simons theory is a purely topological gauge field theory in three spacetime dimensions, introduced in the early 1980s; Witten showed in 1989 that it is exactly soluble and computes knot invariants.
Chernoff bound
The Chernoff bound, also known as Chernoff's inequality, is an exponential upper bound on tail probabilities of random variables, especially sums of independent variables, developed by Herman Chernoff in 1952.
Cherry picking
Cherry picking, also known as suppressing evidence or the cherry-picking fallacy, is selecting only evidence that supports a desired conclusion while omitting data that contradict it.
Chevalley group
A Chevalley group is a finite or algebraic group built from a complex semisimple Lie algebra and a field, introduced by Claude Chevalley in 1955.
Chi-square test of independence
The chi-square test of independence, also called Pearson's chi-square test, is a statistical test determining whether two categorical variables are related, using counts in a contingency table.
Chi-squared distribution
The chi-squared (χ²) distribution is a continuous probability distribution arising from the sum of squares of standard normal variables, widely used in statistics for goodness-of-fit and independence tests.
Chi-squared test
The chi-squared test is a statistical hypothesis test, introduced by Karl Pearson in 1900, that compares observed with expected counts to test goodness of fit and independence.
Chimera state
A chimera state is a dynamical state where some identical coupled oscillators synchronize while others, under the same coupling, stay unsynchronized; observed by Kuramoto and Battogtokh in 2002 and named by Abrams and Strogatz in 2004.
China Family Panel Studies
China Family Panel Studies (CFPS) is a biennial longitudinal survey of Chinese families and individuals, launched in 2010 by Peking University. It tracks economic well-being, education, migration, and health.
Chinese postman problem
The Chinese postman problem, or route inspection problem, asks for the shortest closed walk that traverses every edge of a weighted graph at least once.
Chinese remainder theorem
The Chinese remainder theorem, or Sunzi's theorem, is a number theory result stating that congruences with pairwise coprime moduli always have a solution, unique modulo their product.
Chinese restaurant process
The Chinese restaurant process is a stochastic process in probability theory, devised by Lester Dubins and Jim Pitman in the early 1980s, that generates random partitions by a sequential seating rule.
Chiral algebra
A chiral algebra is an algebraic structure introduced by Alexander Beilinson and Vladimir Drinfeld to formulate the chiral part of two-dimensional conformal field theory, published as Chiral Algebras in 2004.
Choice function
A choice function, introduced by Ernst Zermelo in 1904, is a function that selects exactly one element from each set in a family of nonempty sets.
Cholesky decomposition
The Cholesky decomposition, also called Cholesky factorization, uniquely expresses a symmetric positive definite matrix as A = R^T R and is used to solve linear systems stably.
Chomsky hierarchy
The Chomsky hierarchy is a four-level classification of formal grammars and their language classes, introduced by Noam Chomsky in 1959, nesting from regular to recursively enumerable languages.
Choquet integral
The Choquet integral is an aggregation operator that integrates a function with respect to a non-additive capacity, so criteria can interact; it is used in multi-criteria decision analysis and machine learning.
Chord (geometry)
A chord, also known as a circular chord, is the straight line segment joining two points on a curve, most often a circle; the longest chord of a circle is its diameter.