Mathematics and statistics

Weight lattice

The weight lattice is the lattice of vectors pairing integrally with every coroot of a root system; its dominant weights classify the irreducible finite-dimensional representations of a semisimple Lie algebra.

Weighted arithmetic mean

The weighted arithmetic mean is an average in which each value is multiplied by a weight reflecting its importance, reducing to the ordinary mean when weights are equal.

Weighted correlation network analysis

Weighted correlation network analysis, also known as weighted gene co-expression network analysis, is a statistical method that groups correlated genes into modules and identifies hub genes.

Weighted least squares

Weighted least squares (WLS), also known as weighted linear least squares, is a regression method that weights each observation by its precision, generalizing ordinary least squares.

Weighted median

The weighted median is a robust statistic that generalizes the median by weighting each observation, proposed by F. Y. Edgeworth in 1888 and used in filtering, metrology, and federated learning.

Weighted product method

The weighted product method (WPM) is a multi-criteria decision-making technique that ranks alternatives by multiplying normalized scores raised to criterion weights, the multiplicative counterpart of the weighted sum model.

Weighted regression (statistics)

Weighted regression, most commonly weighted least squares (WLS), fits a regression model by giving each observation its own weight, so that more precise observations count more.

Weil conjectures

The Weil conjectures are four statements, proposed by André Weil in 1949, about the zeta function of an algebraic variety over a finite field, all proved.

Weil group

The Weil group is a locally compact group attached to a local or global field that refines its absolute Galois group by tracking Frobenius with integral exponents.

Weil representation

The Weil representation, also called the Segal–Shale–Weil or metaplectic representation, is a projective representation of the symplectic group that becomes genuine on its double cover; André Weil introduced it in 1964 to interpret theta functions.

Weisfeiler–Leman test

The Weisfeiler–Leman test, also spelled Weisfeiler–Lehman and abbreviated WL or k-WL, is a family of combinatorial algorithms that iteratively color graph vertices to distinguish non-isomorphic graphs.

Welch's t-test

Welch's t-test, also called the unequal-variances t-test, tests whether two independent samples differ in mean by estimating variances separately; B. L. Welch introduced it in 1938.

Well-formed formula

A well-formed formula, abbreviated WFF and pronounced "whiff", is a finite sequence of symbols constructed according to the grammar of a formal language like propositional or first-order logic.

Well-order

A well-order (well-ordering) is a linear order on a set in which every non-empty subset has a least element, exemplified by the usual order on the natural numbers.

Well-ordering theorem

The well-ordering theorem, or well-ordering axiom, states that every set can be given a well ordering. Proved by Ernst Zermelo in 1904, it is equivalent to the axiom of choice over ZF.

Well-posedness of stochastic differential equations

Well-posedness of stochastic differential equations means an SDE has a solution unique in a specified sense, with classical conditions due to Itô and counterexamples like Tanaka's equation.

WENO scheme

A WENO (weighted essentially non-oscillatory) scheme is a high-order finite-difference or finite-volume method for equations with shocks, first introduced in 1994 and widely used in computational fluid dynamics.

Wess–Zumino–Witten model

The Wess–Zumino–Witten model (WZW model, WZNW model) is an exactly solvable two-dimensional conformal field theory whose fields map a closed surface into a Lie group, named for Wess, Zumino, Novikov, and Witten.

Weyl algebra

The Weyl algebra, denoted A_n(K), is the non-commutative algebra of differential operators with polynomial coefficients, named for Hermann Weyl, central to D-module theory and quantum mechanics.

Weyl character formula

The Weyl character formula, also known as the Weyl formula, expresses the character of any irreducible representation of a semisimple Lie algebra as a quotient of alternating sums over the Weyl group.

Weyl group

The Weyl group is the finite group of symmetries of a root system, generated by reflections, and central to the representation theory of Lie groups.

Weyl group of a Kac–Moody algebra

The Weyl group of a Kac–Moody algebra is the Coxeter group generated by simple reflections on the dual Cartan subalgebra, finite exactly when the algebra has finite type.

Weyl tensor

The Weyl tensor is the traceless part of the Riemann curvature tensor, unchanged by conformal rescaling of the metric. It was constructed by Hermann Weyl in 1918.

Weyl's theorem on complete reducibility

Weyl's theorem on complete reducibility is a theorem in representation theory stating that every finite-dimensional representation of a semisimple Lie algebra is a direct sum of irreducible representations.

Wheat and chessboard problem

The wheat and chessboard problem, also called the rice and chessboard problem, is a mathematical exercise where grains double on each square, totaling 18 quintillion grains across 64 squares.

Wheel graph

A wheel graph is a graph formed from a cycle plus one hub vertex connected to every cycle vertex, with rim, spokes, and a wheel-like drawing.

White noise

White noise, also called a white noise process, is a random signal with a flat power spectral density, meaning equal power per unit of bandwidth at every frequency.

Whitehead problem

The Whitehead problem, asked by J.H.C. Whitehead around 1950, asks whether every abelian group with Ext(A, Z) = 0 is free; Shelah proved it independent of ZFC in 1974.

Whitehead's lemma (Lie algebra)

Whitehead's lemma is a pair of theorems of J. H. C. Whitehead stating that the first and second cohomology groups of a finite-dimensional semisimple Lie algebra vanish.