6,052 articles
E8 (mathematics)
E8 (Lie group E8, E8 Lie algebra) is the largest of the five exceptional simple Lie algebras, a 248-dimensional structure of continuous symmetry with 240 roots.
E8 lattice
The E8 lattice, also called the Gosset lattice, is the unique even, unimodular lattice in 8 dimensions, generated by the 240 roots of the E8 root system.
Earth mover's distance
The earth mover's distance (EMD), also called the Wasserstein-1 distance, is a distance between probability distributions, defined as the minimum cost of moving mass from one to the other.
Easton's theorem
Easton's theorem is a result in set theory, proved by William Easton, stating that the continuum function at regular cardinals is constrained only by monotonicity and König's theorem.
Eccentricity (mathematics)
Eccentricity, in mathematics, is a single number measuring how much a conic section deviates from a circle: 0 is a circle, 1 a parabola, above 1 a hyperbola.
Ecological fallacy
The ecological fallacy is the error of treating a relationship observed between groups as holding for the individuals within them, as in Robinson's 1950 census study.
Economic Census (United States)
The Economic Census is the official five-year measure of American business conducted by the U.S. Census Bureau for years ending in 2 and 7, benchmarking GDP and the Producer Price Index.
Edge coloring
Edge coloring assigns colors to a graph's edges so that edges meeting at a common endpoint get different colors; the chromatic index is the minimum number of colors required.
Edge connectivity
Edge connectivity, also called line connectivity, is a graph invariant that counts the minimum number of edges whose deletion disconnects a graph, measuring network robustness.
Edgeworth expansion
The Edgeworth expansion is an asymptotic expansion approximating the distribution or density of a standardized statistic, such as a sample mean, as a normal distribution plus correction terms.
Educational attainment in the United States
Educational attainment in the United States is the highest level of education a person has completed, as measured by the Census Bureau through the census and American Community Survey.
Effect size
Effect size is a quantitative measure of how large a difference or relationship in a study is, reported in original units or standardized forms such as Cohen's d.
Effective descriptive set theory
Effective descriptive set theory is the lightface study of effective Borel, analytic, and co-analytic sets on recursive Polish spaces, merging classical descriptive set theory with Kleene's recursion theory.
Effective dose (pharmacology)
The effective dose in pharmacology is the amount of a drug that produces a defined therapeutic effect; the median effective dose (ED50) produces it in 50% of the population.
Effective sample size
Effective sample size (ESS) is a diagnostic for Markov chain Monte Carlo expressing how many independent draws would carry the same estimation information as autocorrelated draws obtained.
Efficiency (statistics)
Efficiency in statistics measures how well an estimator or statistical test uses sample information, typically by comparing variance against the Cramér–Rao lower bound, the minimum any unbiased estimator can achieve.
Efficient estimator
An efficient estimator is an unbiased estimator whose variance attains the Cramér–Rao lower bound, the smallest variance any unbiased estimator can have, making it a minimum-variance unbiased estimator.
EGARCH model
The EGARCH model, introduced by Daniel B. Nelson in Econometrica in 1991, is a time-series model in which negative and positive shocks of equal size affect volatility differently.
Egger's test
Egger's test is a linear regression test for funnel plot asymmetry in meta-analysis, proposed by Matthias Egger and colleagues in 1997 to detect small-study effects that may indicate publication bias.
Ehrenfeucht–Fraïssé game
The Ehrenfeucht–Fraïssé game (EF game) is a two-player game on two structures in which Spoiler tries to expose differences and Duplicator tries to match every move.
Ehrhart polynomial
The Ehrhart polynomial of a lattice polytope counts lattice points in its dilates, proved a polynomial by Eugène Ehrhart in 1962 and generalized to higher dimensions by Pick's theorem.
Eigendecomposition of a matrix
Eigendecomposition, or eigenvalue decomposition, is the factorization of a square matrix as A = XΛX⁻¹ with eigenvectors; it exists when the matrix has an eigenbasis and underlies PCA and quantum mechanics.
Eigenfunction
An eigenfunction is a nonzero function that a linear operator reproduces as a scalar multiple of itself, the function-space analog of an eigenvector of a matrix.
Eigenvalue
An eigenvalue is a scalar satisfying Az = λz for a nonzero eigenvector z of a matrix A, meaning the transformation stretches that vector without rotating it.
Eigenvalue algorithm
An eigenvalue algorithm is a numerical method for computing eigenvalues of a matrix, using dense methods like the QR algorithm or iterative methods for large sparse matrices.
Eigenvalue interlacing
Eigenvalue interlacing is a linear algebra theorem stating that the eigenvalues of a Hermitian matrix and those of any principal submatrix must alternate in a fixed order.
Eigenvalues and eigenvectors
Eigenvalues and eigenvectors, also called characteristic roots, are scalars and nonzero vectors of a square matrix or operator satisfying Ax = λx, so the matrix only stretches the vector's length.
Eight dimensions of quality
The eight dimensions of quality is a framework proposed by David A. Garvin in 1987 covering performance, features, reliability, conformance, durability, serviceability, aesthetics, and perceived quality.
Eight queens puzzle
The eight queens puzzle, also known as the n-queens problem, asks for placements of chess queens that do not attack each other; it has 92 solutions.
Einstein manifold
An Einstein manifold is a manifold with a pseudo-Riemannian metric whose Ricci tensor is proportional to the metric, the analog of vacuum solutions of general relativity's field equations.