Physical world and mathematics

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 intensity mapping (LIM) is an observational technique that maps integrated spectral-line emission from unresolved galaxies and the diffuse intergalactic medium, tracing large-scale structure across nearly the universe's entire history.

Line profile analysis

Line profile analysis (LPA, XLPA for the X-ray version) is a diffraction method that extracts crystallite size, microstrain, and dislocation density from diffraction peak shapes rather than peak positions.

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-of-sight propagation

Line-of-sight propagation is the transmission of radio, microwave, or optical signals along a direct, unobstructed path from transmitter to receiver, the dominant mode for microwave, satellite, and laser links.

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.

Lineament analysis

Lineament analysis is a remote sensing and structural geology method that maps linear surface features such as faults from satellite imagery and DEMs to infer subsurface geological structure.

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 alkylbenzene

Linear alkylbenzene (LAB) is a family of colorless organic compounds, a benzene ring attached to a straight-chain alkyl group, made industrially as the intermediate for the biodegradable detergent surfactant linear alkylbenzene sulfonate.

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 combination of atomic orbitals

The linear combination of atomic orbitals (LCAO) is a quantum chemistry method that expresses each molecular orbital as a weighted sum of atomic orbital basis functions.

Linear combination of unitaries

The linear combination of unitaries (LCU) is a quantum-computing technique that implements non-unitary operations as weighted sums of unitaries, introduced for Hamiltonian simulation by Childs and Wiebe in 2012.

Linear dichroism

Linear dichroism is the difference in a sample's absorption of light linearly polarized in two perpendicular directions, used to study molecular orientation in DNA, proteins, liquid crystals, and solids.

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 elasticity

Linear elasticity is the branch of continuum mechanics describing how solids deform under small loads, with stress proportional to strain via Hooke's law and governed by the Navier-Cauchy equations.

Linear energy transfer

Linear energy transfer (LET) is a measure of the energy a charged particle transfers locally to matter per unit track length, central to radiobiology and radiation therapy.

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.

Linear logic

Linear logic is a substructural logic introduced by Jean-Yves Girard in 1987 that treats formulas as resources, dropping contraction and weakening so each assumption must be used exactly once.

Linear map

A linear map, also called a linear transformation, is a function between vector spaces that preserves addition and scalar multiplication, exemplified by rotations and projections.

Linear model

A linear model is a statistical model that expresses a response variable as a linear combination of predictors with unknown coefficients, written Y = Xβ + ε and fitted by least squares.

Linear momentum

Linear momentum is the vector quantity p = mv, the product of mass and velocity, whose rate of change equals the applied force in Newton's second law.

Linear motion

Linear motion, also called rectilinear motion, is motion along a single straight line, such as a car on a straight road or a falling ball, studied in kinematics.

Linear no-threshold model

The linear no-threshold (LNT) model assumes any dose of ionizing radiation above zero proportionally increases cancer risk, underpinning radiation safety rules and the ALARA principle.