42,772 articles
General linear group
The general linear group GL_n(R) is the group of all invertible n by n matrices over a ring R, forming a group under matrix multiplication.
General linear model
The general linear model, or multivariate linear regression, is the statistical framework Y = Xβ + ε that underlies t-tests, ANOVA, ANCOVA, and regression, estimated by ordinary least squares.
General number field sieve
The general number field sieve (GNFS) is the fastest known classical algorithm for factoring arbitrary large integers, generalized by Buhler, Lenstra, and Pomerance in 1993 and used for RSA-250.
General recursive function
A general recursive function, also called a μ-recursive or partial recursive function, is built from basic functions using composition, primitive recursion, and unbounded minimization, formalizing effective computability.
General relativistic magnetohydrodynamics
General relativistic magnetohydrodynamics (GRMHD) combines magnetohydrodynamics with general relativity to describe magnetized plasma in curved spacetime, modeling black hole accretion, relativistic jets, and neutron star mergers.
General relativity
General relativity, also called the general theory of relativity, is Albert Einstein's 1915 theory that gravity is the curvature of spacetime; it passes every experimental test to date.
General Roman Calendar
The General Roman Calendar, also called the Roman calendar of saints, is the liturgical calendar of the Roman Rite, promulgated by Pope Paul VI in 1969.
General Scholium
The General Scholium (Scholium Generale) is the essay Isaac Newton appended to the 1713 second edition of the Principia, attacking Cartesian vortices and framing his design argument.
General Social Survey
The General Social Survey is a nationally representative survey of US adults conducted by NORC at the University of Chicago since 1972, tracking social attitudes over time.
General theory of Banach algebras
The general theory of Banach algebras, which began in 1941, examines complete normed algebras with submultiplicative norms. It details concepts like closed ideals, quotients, and the Gelfand transform.
General-relativistic magnetohydrodynamic simulations of black hole accretion
General-relativistic magnetohydrodynamic (GRMHD) simulations numerically model magnetized plasma accreting onto black holes, underlying Event Horizon Telescope interpretations of Sgr A and M87 in SANE and MAD states.
Generalizability theory
Generalizability theory is a statistical framework that estimates the reliability of measurements by separating multiple sources of error, introduced by Cronbach, Rajaratnam, and Gleser in 1963.
Generalization
Generalization is extending a finding from the studied sample to a broader population, a component of external validity in research and a key goal in machine learning.
Generalizations of Fibonacci numbers
Generalizations of Fibonacci numbers, including the k-bonacci or k-step Fibonacci numbers, are integer sequences that extend the Fibonacci recurrence by summing more preceding terms, giving tribonacci and tetranacci numbers.
Generalized additive model
A generalized additive model (GAM) is a regression model in which each covariate enters through a smooth function estimated from the data, introduced by Hastie and Tibshirani in 1986.
Generalized Approximate Message Passing
Generalized approximate message passing (GAMP) is an iterative Bayesian estimation algorithm introduced by Sundeep Rangan in 2010 that recovers signals through linear transforms, widely used in compressed sensing.
Generalized Cartan matrix
A generalized Cartan matrix, plural Cartan matrices, is a square integer matrix with diagonal entries 2 and non-positive off-diagonal entries; each one determines a Kac-Moody Lie algebra.
Generalized continuum hypothesis
The generalized continuum hypothesis (GCH) is the set-theoretic statement that each infinite cardinal's power set has the next larger cardinality; Gödel and Cohen proved it independent of ZFC.
Generalized coordinates
Generalized coordinates are independent parameters, written q1, q2, and so on, that specify the configuration of a mechanical system and form the backbone of Lagrangian mechanics, developed by Lagrange.
Generalized coordination number
The generalized coordination number (GCN) is a geometric descriptor in computational catalysis that weighs each of an atom's neighbors by its own coordination to predict adsorption energies.
Generalized cross-validation
Generalized cross-validation (GCV) is a criterion for choosing a smoothing or regularization parameter in linear models, introduced by Craven and Wahba in 1979 and computable from a single fit without retraining.
Generalized eigenvector
A generalized eigenvector of a matrix A is a nonzero vector v with (A − λI)^p v = 0 for some p; ordinary eigenvectors are the case p = 1.
Generalized entropy
Generalized entropy is the sum of the Bekenstein-Hawking area term and the von Neumann entropy of quantum fields outside a surface. Bekenstein introduced the idea in 1973.
Generalized estimating equation
A generalized estimating equation (GEE) is a statistical method for estimating regression coefficients when observations are correlated, as in repeated measurements, introduced by Liang and Zeger in 1986.
Generalized estimating equations
Generalized estimating equations (GEE) is a statistical method introduced by Liang and Zeger in 1986 for fitting regression models to correlated or longitudinal data, robust to misspecified within-cluster correlation.
Generalized extreme value distribution
The generalized extreme value (GEV) distribution is a three-parameter family of probability distributions that models the largest value in blocks, such as annual maxima of floods.
Generalized Kac–Moody algebra
A generalized Kac–Moody algebra, also called a Borcherds or BKM algebra, is an infinite-dimensional Lie algebra introduced by Richard Borcherds in 1988, generalizing Kac–Moody algebras by allowing imaginary simple roots.
Generalized least squares
Generalized least squares (GLS) is a method for estimating linear regression coefficients when errors are correlated or have unequal variance, introduced by A. T. Aitken in 1935.
Generalized likelihood ratio test
The generalized likelihood ratio test (GLRT) is a statistical hypothesis test that compares maximized likelihoods under null and alternative models, calibrated by Wilks' chi-square theorem.
Generalized linear mixed model
A generalized linear mixed model (GLMM) is a regression model that extends the generalized linear model with random effects, widely used in biostatistics, ecology, and agronomy.