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Что (кто) такое linear ordering - определение

ORDERING RELATION WHERE ALL ELEMENTS CAN BE COMPARED, EQUALITY MEANS IDENTITY; BINARY RELATION ON SOME SET, WHICH IS ANTISYMMETRIC, TRANSITIVE, AND TOTAL

Infinite descending chain; TotalOrderedSet; Total ordered set; Totally ordered set; Linear order; Total ordering relation; Total ordering; Linearly ordered set; Totally ordered; Linear ordering; Linearly ordered; Chain (order theory); Total (order theory); Toset; Linear (order); Infinite descending chains; Strict total order; Totally-ordered set; Finite chain; Strict linear order; Finite total order; Simple order; Simply ordered set; Complete total order; Chain (ordered set); Complete ordering; Complete order; Ascending chain; Loset; Chain (poset)

Найдено результатов: 951

totally ordered

<mathematics> Having a total ordering. (1997-01-10)

linear map

$The function f:\R^2 \to \R^2 with f(x, y) = (2x, y) is a linear map. This function scales the x component of a vector by the factor 2.$
$The function f(x, y) = (2x, y) is additive: It doesn't matter whether vectors are first added and then mapped or whether they are mapped and finally added: f(\mathbf a + \mathbf b) = f(\mathbf a) + f(\mathbf b)$
$The function f(x, y) = (2x, y) is homogeneous: It doesn't matter whether a vector is first scaled and then mapped or first mapped and then scaled: f(\lambda \mathbf a) = \lambda f(\mathbf a)$

MAPPING THAT PRESERVES THE OPERATIONS OF ADDITION AND SCALAR MULTIPLICATION

Linear operator; Linear mapping; Linear transformations; Linear operators; Linear transform; Linear maps; Linear isomorphism; Linear isomorphic; Linear Transformation; Linear Transformations; Linear Operator; Homogeneous linear transformation; User:The Uber Ninja/X3; Linear transformation; Bijective linear map; Nonlinear operator; Linear Schrödinger Operator; Vector space homomorphism; Vector space isomorphism; Linear extension of a function; Linear extension (linear algebra); Extend by linearity; Linear endomorphism

<mathematics> (Or "linear transformation") A function from a vector space to a vector space which respects the additive and multiplicative structures of the two: that is, for any two vectors, u, v, in the source vector space and any scalar, k, in the field over which it is a vector space, a linear map f satisfies f(u+kv) = f(u) + kf(v). (1996-09-30)

total ordering

<mathematics> A relation R on a set A which is a {partial ordering}; i.e. it is reflexive (xRx), transitive (xRyRz => xRz) and antisymmetric (xRyRx => x=y) and for any two elements x and y in A, either x R y or y R x. See also equivalence relation, well-ordered. (1995-02-16)

Linear map

$The function f:\R^2 \to \R^2 with f(x, y) = (2x, y) is a linear map. This function scales the x component of a vector by the factor 2.$
$The function f(x, y) = (2x, y) is additive: It doesn't matter whether vectors are first added and then mapped or whether they are mapped and finally added: f(\mathbf a + \mathbf b) = f(\mathbf a) + f(\mathbf b)$
$The function f(x, y) = (2x, y) is homogeneous: It doesn't matter whether a vector is first scaled and then mapped or first mapped and then scaled: f(\lambda \mathbf a) = \lambda f(\mathbf a)$

MAPPING THAT PRESERVES THE OPERATIONS OF ADDITION AND SCALAR MULTIPLICATION

Linear operator; Linear mapping; Linear transformations; Linear operators; Linear transform; Linear maps; Linear isomorphism; Linear isomorphic; Linear Transformation; Linear Transformations; Linear Operator; Homogeneous linear transformation; User:The Uber Ninja/X3; Linear transformation; Bijective linear map; Nonlinear operator; Linear Schrödinger Operator; Vector space homomorphism; Vector space isomorphism; Linear extension of a function; Linear extension (linear algebra); Extend by linearity; Linear endomorphism

In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism.

https://en.wikipedia.org/wiki/Linear_map

linear transformation

$The function f:\R^2 \to \R^2 with f(x, y) = (2x, y) is a linear map. This function scales the x component of a vector by the factor 2.$
$The function f(x, y) = (2x, y) is additive: It doesn't matter whether vectors are first added and then mapped or whether they are mapped and finally added: f(\mathbf a + \mathbf b) = f(\mathbf a) + f(\mathbf b)$
$The function f(x, y) = (2x, y) is homogeneous: It doesn't matter whether a vector is first scaled and then mapped or first mapped and then scaled: f(\lambda \mathbf a) = \lambda f(\mathbf a)$

MAPPING THAT PRESERVES THE OPERATIONS OF ADDITION AND SCALAR MULTIPLICATION

Linear operator; Linear mapping; Linear transformations; Linear operators; Linear transform; Linear maps; Linear isomorphism; Linear isomorphic; Linear Transformation; Linear Transformations; Linear Operator; Homogeneous linear transformation; User:The Uber Ninja/X3; Linear transformation; Bijective linear map; Nonlinear operator; Linear Schrödinger Operator; Vector space homomorphism; Vector space isomorphism; Linear extension of a function; Linear extension (linear algebra); Extend by linearity; Linear endomorphism

linear map

totally ordered set

<mathematics> A set with a total ordering.

Total order

In mathematics, a total or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation \leq on some set X, which satisfies the following for all a, b and c in X:

https://en.wikipedia.org/wiki/Total_order

Linear referencing

METHOD OF SPATIAL REFERENCING

Linear Referencing System; Linear Reference System; Linear-referencing; Linear Referencing; Linear reference system; Linear referencing system; Linearly referenced

Linear referencing, also called linear reference system or linear referencing system (LRS), is a method of spatial referencing in engineering and construction, in which the locations of physical features along a linear element are described in terms of measurements from a fixed point, such as a milestone along a road. Each feature is located by either a point (e.

https://en.wikipedia.org/wiki/Linear_referencing

Linear inequality

INEQUALITY WHICH INVOLVES A LINEAR FUNCTION

Set of linear inequalities; Systems of linear inequalities; System of linear inequalities; Linear inequalities; Linear Inequality

In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality:.

https://en.wikipedia.org/wiki/Linear_inequality

Linear model

TYPE OF STATISTICAL MODEL

Linear models; Linear Models

In statistics, the term linear model is used in different ways according to the context. The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model.

https://en.wikipedia.org/wiki/Linear_model

Википедия

Total order

In mathematics, a total or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation $\leq$ on some set $X$ , which satisfies the following for all $a,b$ and $c$ in $X$ :

$a\leq a$ (reflexive).
If $a\leq b$ and $b\leq c$ then $a\leq c$ (transitive).
If $a\leq b$ and $b\leq a$ then $a=b$ (antisymmetric).
$a\leq b$ or $b\leq a$ (strongly connected, formerly called total).

Reflexivity (1.) already follows from connectedness (4.), but is required explicitly by many authors nevertheless, to indicate the kinship to partial orders. Total orders are sometimes also called simple, connex, or full orders.

A set equipped with a total order is a totally ordered set; the terms simply ordered set, linearly ordered set, and loset are also used. The term chain is sometimes defined as a synonym of totally ordered set, but refers generally to some sort of totally ordered subsets of 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.

https://en.wikipedia.org/wiki/Total order