In order theory, a branch of mathematics, a linear extension of a partial order is a total order (or linear order) that is compatible with the partial...

below. The resulting extension remains linear and bounded, and is thus continuous, which makes it a continuous linear extension. This procedure is known...

specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function)...

a given partially ordered set. An extension of a given partial order to a total order is called a linear extension of that partial order. For delimitation...

case that x ≤ ∗ y . {\displaystyle x\leq ^{*}y.} A linear extension is an extension that is also a linear (that is, total) order. As a classic example, the...

Kolmogorov extension theorem, in probability theory Linear extension, in order theory Sheaf extension, in algebraic geometry Tietze extension theorem, in...

the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace of some vector space...

science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge (u,v) from vertex...

In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete...

In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars...

a normal extension is an algebraic field extension L/K for which every irreducible polynomial over K that has a root in L splits into linear factors over...

related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector...

relationship, a ≤ b, has three linear extensions, a ≤ b ≤ c, a ≤ c ≤ b, and c ≤ a ≤ b. In all three of these extensions, a is earlier than b. However,...

{E} \left[\int _{0}^{t}H_{s}^{2}\,ds\right].} By a continuous linear extension, the integral extends uniquely to all predictable integrands satisfying...

In statistics, linear regression is a model that estimates the relationship between a scalar response (dependent variable) and one or more explanatory...

with itself. The lexicographic combination of two total orders is a linear extension of their product order, and thus the product order is a subrelation...

Calculus of Extension, Internet Archive Grassmann, Hermann (1844), Die Lineale Ausdehnungslehre – Ein neuer Zweig der Mathematik (in German) (The Linear Extension...

generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model...

has length 1, etc. Linear. See total order. Linear extension. A linear extension of a partial order is an extension that is a linear order, or total order...

Grassmann published his "Theory of Extension" which included foundational new topics of what is today called linear algebra. In 1848, James Joseph Sylvester...

Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical...

analysis on a topological vector space X {\displaystyle X} , a (possibly non-linear) operator T : X → X ∗ {\displaystyle T:X\rightarrow X^{*}} is said to be...

if and only if it has distinct roots in any extension of F. That is, if it is the product of distinct linear factors X - a in some algebraic closure of...

contrast, linear algebra deals mostly with finite-dimensional spaces, and does not use topology. An important part of functional analysis is the extension of...

theory, a forking extension of a type is an extension of that type that is not free[clarify] whereas a non-forking extension is an extension that is as free...

1961–1964 – Graham completed a new series of paintings referred to as Linear Extensions. 1964–1973 – Graham conducted experimental studies based on a new...

measure linear position and velocity using a flexible cable and spring-loaded spool. Other common names include string pot, cable-extension transducer...

In linear algebra, the transpose of a linear map between two vector spaces, defined over the same field, is an induced map between the dual spaces of...

completely factors into linear factors over L. Every algebraic extension F/K admits a normal closure L, which is an extension field of F such that L /...

statistics, a generalized linear mixed model (GLMM) is an extension to the generalized linear model (GLM) in which the linear predictor contains random...