Mathematics and statistics

Adjugate matrix

The adjugate matrix, also called the classical adjoint, is the transpose of a square matrix's cofactor matrix; multiplying it by the matrix gives det(A) times the identity, which yields the inverse.

Adjusted Rand index

The Adjusted Rand index (ARI) is a chance-adjusted measure comparing two clusterings of the same items, equaling 1.0 for identical partitions and near 0.0 for random labelings.

ADMB

ADMB (AD Model Builder) is a free, open source software suite for non-linear statistical modeling, created by David Fournier in the 1980s and widely used in fisheries science.

Admissibility (statistics)

Admissibility in statistics means a decision rule, such as an estimator, is not dominated: no other rule has risk at least as small everywhere and strictly smaller somewhere.

Admissible set

An admissible set is a transitive set whose membership relation models Kripke–Platek set theory, a weak ZF fragment; the hereditarily finite sets are the smallest example.

Adolphe Quetelet

Adolphe Quetelet was a Belgian astronomer and statistician who founded the Brussels Observatory and created the Body Mass Index and the concept of the average man.

The Adomian decomposition method (ADM) is a semi-analytical technique for solving nonlinear differential and integral equations by expressing the solution as a series built recursively with Adomian polynomials, requiring no linearization or discretization.

Oct 21, 2026

ADOPT study

ADOPT (Accurate Display of Postpartum Hemorrhage Using Triton), NCT02981758, a Hackensack Meridian Health retrospective blinded cohort study comparing visual estimated blood loss with Triton-quantified blood loss in 300 vaginal deliveries, 2016-2019; distinct from the ADOPT diabetes trial and IGNITE ADOPT PGx.

Adrien-Marie Legendre

Adrien-Marie Legendre, sometimes Adrien Legendre, was a French mathematician (1752–1833) known for the method of least squares, the Legendre symbol, and his theory of elliptic integrals.

AF algebra

An AF algebra, or approximately finite-dimensional algebra, is a C-algebra built as an inductive limit of finite-dimensional C-algebras; Elliott classified them in 1976 by their ordered K0-groups.

Affine arithmetic

Affine arithmetic is a self-validated numerical computation model, proposed by Comba and Stolfi in 1993, that tracks correlations between uncertain quantities for tighter error bounds than interval arithmetic.

Affine connection

An affine connection is a differential-geometric structure on a smooth manifold that defines covariant derivatives, parallel transport, and geodesics; Hermann Weyl introduced it in 1918.

Affine geometry

Affine geometry is the branch of geometry studying properties preserved by affine transformations, which keep parallelism and ratios along lines but not distance or angle.

Affine group

The affine group of a vector space is the group of all affine transformations, maps x ↦ Ax + b combining invertible linear maps with translations.

Affine Lie algebra

An affine Lie algebra, also called an affine Kac-Moody algebra, is an infinite-dimensional Lie algebra that is a central extension of the loop algebra of a semisimple Lie algebra.

Affine plane

An affine plane is an incidence structure of points and lines in which any two points lie on exactly one line and parallel lines exist.

Affine root system

An affine root system is an infinite root system whose quotient is a finite root system, underlying affine Kac–Moody Lie algebras and classified by Macdonald in 1972.

Affine space

An affine space is a set of points on which a vector space acts as translations, so point differences are vectors but points cannot be added or compared to a fixed origin.

Affine subspace

An affine subspace is a subset of a vector space formed by shifting a linear subspace away from the origin; it equals the solution set of a system of linear equations.

Affine transformation

An affine transformation is a geometric mapping combining a linear transformation such as rotation, scaling, or shear with a translation, preserving straightness, parallelism, and ratios along parallel lines.

Affine variety

An affine variety is a subset of affine space defined as the common zero set of a collection of polynomials, the basic object of classical algebraic geometry.

Affine variety of parallelism

The affine variety of parallelism is the parallelism structure of affine geometry, splitting lines into parallel classes, one per direction; adding a point at infinity for each class yields a projective plane.

Afghan refugees

Afghan refugees are nationals of Afghanistan who fled, mainly to Iran and Pakistan, after the 1978 coup and 1979 Soviet invasion, in one of the world's largest displacements.

African vulture optimization algorithm

The African vulture optimization algorithm, or AVOA, is a population-based metaheuristic that mimics African vultures' foraging to find global optima, introduced by Abdollahzadeh, Gharehchopogh, and Mirjalili in 2021.

Age-period-cohort analysis

Age-period-cohort analysis is a statistical method for estimating the separate effects of age, time period, and birth cohort on outcomes such as disease rates in population data.

Age–period–cohort model

The age–period–cohort (APC) model is a statistical model that decomposes trends in rates into age, calendar period, and birth cohort effects, used in demography, epidemiology, and social science.

Agricultural land

Agricultural land, also called farmland, is land used for agriculture: arable land, permanent crops, and pastures, covering about a third of the world's land area.

Airy function

The Airy functions Ai(z) and Bi(z) are the two standard independent solutions of Airy's equation w'' = zw, introduced by George Biddell Airy in his 1838 work on light near a caustic.

AIXI

AIXI, also written AIξ, is a theoretical mathematical model of an optimal reinforcement learning agent, constructed by Marcus Hutter by combining Solomonoff induction with sequential decision theory.