6,052 articles
Limit ordinal
A limit ordinal is a nonzero ordinal number that has no immediate predecessor, so it is not the successor of any ordinal; the first example is ω, the smallest infinite ordinal.
Limit point
A limit point, also called an accumulation point or cluster point, of a set is a point every neighborhood of which contains a point of the set other than itself.
Limit superior and limit inferior
The limit superior (limsup) and limit inferior (liminf) of a real sequence are its eventual upper and lower bounds, obtained from the suprema and infima of its tails.
Limited information maximum likelihood
Limited information maximum likelihood (LIML) is a single-equation instrumental-variable estimator for a structural equation in a simultaneous-equations system, introduced by Anderson and Rubin in 1949.
Limits of agreement
Limits of agreement are the range, mean difference plus or minus 1.96 standard deviations, within which 95% of differences between two measurement methods are expected to lie.
Lin Lin
Lin Lin is a Chinese-American applied mathematician who joined UC Berkeley's mathematics department in 2014, known for numerical methods for electronic structure, quantum many-body problems, and quantum computing algorithms.
Lindeberg's condition
Lindeberg's condition is a condition on triangular arrays of independent random variables requiring no single summand to dominate the total variance, yielding a normal limit for normalized row sums.
Lindelöf hypothesis
The Lindelöf hypothesis, also known as the Lindelöf conjecture, is a 1908 conjecture of Ernst Leonard Lindelöf asserting the Riemann zeta function grows slowly on the critical line.
Lindemann–Weierstrass theorem
The Lindemann–Weierstrass theorem is a result in transcendental number theory, proved by Karl Weierstrass in 1885, stating that exponentials of distinct algebraic numbers are linearly independent over the algebraic numbers.
Lindenbaum–Tarski algebra
The Lindenbaum–Tarski algebra, also called the Lindenbaum algebra, is the algebra of formulas of a logic modulo provable equivalence, introduced by Lindenbaum and Tarski in 1926–27.
Lindström's theorem
Lindström's theorem, proved by the Swedish logician Per Lindström in 1969, characterizes first-order logic as maximal in expressive power among logics satisfying compactness and the Löwenheim–Skolem theorem.
Lindy effect
The Lindy effect, or Lindy's Law, is the statistical tendency for non-perishable things like books and technologies to have longer remaining life expectancy the longer they have existed.
Line (geometry)
In geometry, a line is a straight, one-dimensional extent of points that extends without limit in both directions, and is treated as an undefined term fixed by the axioms.
Line at infinity
The line at infinity is a projective line added to an affine plane, collecting one new point per parallel class, so every pair of distinct lines meets exactly once.
Line bundle
A line bundle is a vector bundle whose fiber at every point is one-dimensional; in algebraic geometry it appears as an invertible sheaf and encodes divisors.
Line chart
A line chart, also called a line graph, is a data visualization that connects data points with line segments, most often to show change over time.
Line graph
The line graph, also called the edge graph or interchange graph, is a graph whose vertices correspond to the edges of a graph G, joined when they share an endpoint.
Line integral
A line integral, also called a curve integral, is an integral of a function evaluated along a curve in a plane or in space rather than along an axis.
Line search
A line search is a subroutine in numerical optimization that picks how far to step along a search direction, using conditions such as Armijo or Wolfe.
Line segment
A line segment, also called a straight-line segment, is the finite part of a straight line between two endpoints, distinguished from lines and rays by having two endpoints.
Line transect
Line transect sampling is a survey method for estimating animal population density: observers walk straight lines, record perpendicular distances to detections, and model how detections decline with distance.
Line–line intersection
Line–line intersection, also called intersection of two lines, finds where two straight lines meet; parallel lines never do, and in 3D lines can be skew.
Linear algebra
Linear algebra is the branch of mathematics that studies vector spaces and linear maps between them, together with the matrices, determinants, and eigenvalues used to compute with them.
Linear canonical transform
The linear canonical transform (LCT) is a three-parameter family of integral transforms generalizing the Fourier, fractional Fourier, and Fresnel transforms, used to model first-order optical systems.
Linear combination
A linear combination is an expression of the form c1v1 + ... + ckvk, formed by scaling vectors and adding them; it underlies span, independence, and bases.
Linear differential equation
A linear differential equation is a differential equation in which the unknown and its derivatives appear only to the first power, never multiplied together or inside nonlinear functions.
Linear equation
A linear equation, also called a first-degree equation, is an algebraic equation where each variable appears only to the first power, as in ax + b = 0.
Linear function
A linear function, also called a linear map or linear transformation, is a function between vector spaces that preserves vector addition and scalar multiplication; it is represented by a matrix.
Linear independence
Linear independence is the property of a set of vectors where no vector is a linear combination of the others; it is half of the definition of a basis.
Linear least squares
Linear least squares is a method of fitting a linear model to data by minimizing the sum of squared deviations between observations and predictions, first published by Legendre in 1805.