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Confirmatory analysis
Confirmatory analysis is a statistical approach that tests hypotheses fixed in advance using formal significance tests or confidence intervals, as required in confirmatory clinical trials for firm evidence of efficacy.
Confirmatory factor analysis
Confirmatory factor analysis (CFA) is a multivariate statistical method that tests whether a pre-specified set of latent factors explains the covariances among observed variables, contrasting with exploratory factor analysis.
Conformal algebra
A conformal algebra is the Lie algebra of infinitesimal conformal transformations of a geometry or field theory, central to conformal field theory and the operator product expansion.
Conformal geometry
Conformal geometry is the branch of geometry studying figures under angle-preserving transformations. By Liouville's theorem, in dimensions three and higher every smooth conformal map is a Möbius transformation.
Conformal map
A conformal map, also called a conformal transformation, is a transformation that preserves angles between curves locally; in complex analysis it is usually a holomorphic map with nonzero derivative.
Conformal prediction
Conformal prediction is a framework in statistics and machine learning that wraps any point-prediction method to produce sets or intervals containing the true outcome with guaranteed probability, assuming only exchangeability.
Confounding
Confounding, also known as statistical confounding, is a distortion of an estimated exposure-outcome association arising when a third factor causes both, absent in randomized trials.
Confusion matrix
A confusion matrix, also known as a matching matrix or error matrix, is a table summarizing classification model performance, cross-tabulating predicted against actual classes, with correct predictions on the diagonal.
Congruence (geometry)
Congruence in geometry is the relation between figures with the same shape and size, meaning one can be transformed into the other by an isometry.
Congruence lattice
The congruence lattice of an algebra is the lattice of all its congruence relations ordered by inclusion, generalizing normal subgroups and ideals; every algebraic lattice arises this way.
Congruence subgroup
A congruence subgroup is a subgroup of the modular group SL2(Z) containing all matrices congruent to the identity modulo some integer N. It underlies modular forms.
Conic programming
Conic programming is an optimization method minimizing a linear objective over linear equations with the variable in a closed convex cone; the cone's choice yields linear, second-order cone, and semidefinite programming.
Conic section
A conic section, also known as a quadratic curve, is the curve formed by a plane cutting a double cone: a circle, ellipse, parabola, or hyperbola.
Conjecture
A conjecture is a mathematical statement proposed as true on the basis of observation or partial evidence but lacking a rigorous proof; a proof makes it a theorem.
Conjugacy class
A conjugacy class is the set of all elements of a group obtainable from one another by conjugation, a = gbg⁻¹; the classes partition the group and underlie the class equation and character theory.
Conjugate gradient method
The conjugate gradient (CG) method is an iterative algorithm for solving symmetric positive definite linear systems Ax = b, introduced by Magnus Hestenes and Eduard Stiefel in 1952.
Conjugate point
A conjugate point is a point on a geodesic where a nonzero Jacobi field vanishes at both endpoints, marking where nearby geodesics refocus; past the first one, a geodesic stops minimizing length.
Conjugate prior
A conjugate prior, also called a conjugate distribution, is a prior distribution whose posterior under a likelihood stays in the same family, a term introduced by Raiffa and Schlaifer in 1961.
Conjugate transpose
The conjugate transpose, also known as the Hermitian transpose or Hermitian conjugate, is the matrix obtained by transposing a complex matrix and taking the complex conjugate of each entry, written A, A^H, or A†.
Conjunction fallacy
The conjunction fallacy, or conjunction effect, is a reasoning error in which a combination of two events is judged more probable than one event alone.
Conjunctive normal form
Conjunctive normal form (CNF), also called clausal normal form, is a standard way of writing a propositional logic formula as a conjunction (AND) of clauses, each a disjunction of literals.
Conjunctive query
A conjunctive query is a database query expressed as a conjunction of relational atoms with existentially quantified variables, defined by Chandra and Merlin in 1977; evaluation is NP-complete.
Connected space
A connected space, also called a connected set or connected topological space, is a topological space that cannot be split into two non-empty disjoint open sets, formalizing a space in one piece.
Connected sum
The connected sum is a topology operation that combines two n-dimensional manifolds into one by removing n-balls and gluing the boundary spheres, written M # N.
Connectivity (graph theory)
Connectivity, also called graph connectivity, is a graph theory invariant measuring how many vertices or edges must be removed to disconnect a graph, central to network design.
Connes classification of type III factors
The Connes classification of type III factors is the 1973 partition of type III von Neumann factors into III₀, IIIλ, and III₁, defined by Alain Connes via the S and T invariants from modular theory.
Connes embedding problem
The Connes embedding problem, also called Connes' embedding conjecture, asked whether every tracial von Neumann algebra embeds into an ultrapower of the hyperfinite II1 factor; it was refuted in 2020.
Consensus clustering
Consensus clustering is a resampling-based clustering method that assesses cluster stability by repeatedly clustering perturbed versions of a dataset, producing a consensus matrix and clustering.
Conservative vector field
A conservative vector field, also called a gradient field or potential field, is one whose line integral between two points depends only on the endpoints, not the path.
Consistency
Consistency, also called logical consistency, is the syntactic property that no contradiction can be proven from a set of formulas; Gödel's completeness theorem shows every consistent first-order set is satisfiable.