Linear extension information

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...

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

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

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. A strict total...

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...

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

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...

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

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 statistics, linear regression is a statistical model which estimates the linear relationship between a scalar response and one or more explanatory...

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

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 in...

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

linear logic (that is linear logic with weakening, an extension rather than a fragment) was shown to be decidable, in 1995. Many variations of linear...

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...

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...

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

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...

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

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

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...

found in linear time, if such a diagram exists. In particular, if the input poset is a graded poset, it is possible to determine in linear time whether...

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 /...

well. The lexicographical order of two totally ordered sets is thus a linear extension of their product order. One can define similarly the lexicographic...

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

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...