Mathematics and statistics

Spatial error model

The spatial error model is a spatial regression model where spatial dependence enters through autocorrelated errors, introduced by Ord in 1975 and popularized by Cliff and Ord in 1981.

Spatial sampling design

Spatial sampling design is the set of procedures for choosing which locations to observe in a geographically distributed population, organized around design-based and model-based inference.

Spearman's rank correlation coefficient

Spearman's rank correlation coefficient, also called Spearman's rho, is a nonparametric statistic measuring how well two variables follow a monotonic relationship, ranging from −1 to +1. Charles Spearman introduced it in 1904.

Specht module

A Specht module is a module for the symmetric group built from Young tableaux of a given partition shape, introduced by Wilhelm Specht in 1935.

Special Data Dissemination Standard

The Special Data Dissemination Standard (SDDS) is a voluntary standard the IMF established in 1996 prescribing how member countries publish economic and financial statistics, created after the Mexican financial crisis.

Special linear group

The special linear group, written SLn, is the group of n by n matrices with determinant 1 over a ring or field, also called the unimodular group.

Special linear Lie algebra

The special linear Lie algebra slₙ consists of n×n matrices with trace zero under the commutator bracket, and is the Lie algebra of the special linear group of determinant-1 matrices.

Special orthogonal group

The special orthogonal group SO(n) is the subgroup of the orthogonal group O(n) with determinant 1, the orientation-preserving rotations of Euclidean space: SO(3) the rotations of three-dimensional space.

Special right triangle

A special right triangle is a right triangle whose angles are either 45-45-90 or 30-60-90, so its side ratios are fixed constants expressible exactly with square roots.

Special unitary group

The special unitary group SU(n), also called the unitary unimodular group, is the group of n × n unitary matrices with determinant 1, of dimension n² − 1.

Specification test (econometrics)

A specification test is a statistical hypothesis test checking whether an econometric model's functional form, moment conditions, and distributional assumptions are consistent with the observed data.

Specker sequence

A Specker sequence is a computable, monotonically increasing, bounded sequence of rational numbers whose limit is an uncomputable real, first given by Ernst Specker in 1949.

Spectral collocation method

The spectral collocation method, also called the pseudospectral method, is a numerical technique for solving differential equations by representing the solution with global basis functions and enforcing the equation exactly at collocation points.

Spectral density

The spectral density, or spectral power density, describes how the power or energy of a signal or random process is distributed over frequency, revealing oscillations and noise hidden in the time domain.

Spectral density estimation

Spectral density estimation is the set of statistical methods for estimating a time series' power spectral density, showing how its variance is distributed across frequency.

Spectral element method

The spectral element method is a numerical technique for solving partial differential equations, combining high-order polynomial basis functions with a finite-element mesh for exponential convergence.

Spectral gap (Markov chain)

The spectral gap of a Markov chain, for a reversible chain equal to 1 minus the second-largest eigenvalue, measures how fast the chain converges to its stationary distribution.

Spectral graph theory

Spectral graph theory is the branch of graph theory that studies graphs through eigenvalues and eigenvectors of their adjacency, degree, and Laplacian matrices, linking algebra to properties like connectivity.

Spectral norm

The spectral norm of a matrix, also called the matrix 2-norm, is the operator norm induced by the Euclidean vector norm, equal to the matrix's largest singular value.

Spectral radius

The spectral radius of a graph is the largest absolute value among the eigenvalues of its adjacency matrix, central to spectral graph theory and epidemic modeling.

Spectral sequence

A spectral sequence is a sequence of differential modules used to compute homology and cohomology groups page by page, introduced by Jean Leray in 1946.

Spectral theorem

The spectral theorem, or eigen decomposition theorem, states that self-adjoint operators decompose into real eigenvalues and an orthonormal basis of eigenvectors, underlying PCA and quantum mechanics.

Spectral triple

A spectral triple is data (A, H, D) encoding a geometric space, the basic object of Alain Connes' noncommutative geometry, where it generalizes Riemannian manifolds with the Dirac operator.

Spectrum (functional analysis)

The spectrum, also called the operator spectrum, is the set of scalars λ for which T − λI has no bounded inverse, generalizing a matrix's eigenvalues.

Spectrum of a ring

The spectrum of a ring, written Spec(R), is the set of all prime ideals of a commutative ring R with the Zariski topology, forming an affine scheme.

Spelling bee

Spelling bee: oral spelling competition, mainly American, in which students spell words aloud until one remains. Best known via the Scripps National Spelling Bee (since 1925); 2026 champion Shrey Parikh set a spell-off record of 32 words in 90 seconds.