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Etymologie

linear invariance - Übersetzung nach russisch

THEOREM IN TOPOLOGY ABOUT HOMEOMORPHIC SUBSETS OF EUCLIDEAN SPACE

Invariance of dimension; Brouwer's theorem on domain invariance; Invariance of domain theorem; Domain invariance theorem

$A map which is not a homeomorphism onto its image: <math>g : (-1.1, 1) \to \R^2</math> with <math>g(t) = \left(t^2 - 1, t^3 - t\right).</math>$

linear invariance

математика

линейная инвариантность

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

['liniətrænsfə'meiʃ(ə)n]

общая лексика

линейное преобразование

linear mapping

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

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

математика

линейное отображение

Definition

linear map

<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)

Weitere Definitionen anzeigen

Wikipedia

Invariance of domain

Invariance of domain is a theorem in topology about homeomorphic subsets of Euclidean space $\mathbb {R} ^{n}$ . It states:

If

U

is an open subset of

\mathbb {R} ^{n}

and

f:U\rightarrow \mathbb {R} ^{n}

is an injective continuous map, then

V:=f(U)

is open in

\mathbb {R} ^{n}

and

f

is a homeomorphism between

U

and

V

.

The theorem and its proof are due to L. E. J. Brouwer, published in 1912. The proof uses tools of algebraic topology, notably the Brouwer fixed point theorem.

https://en.wikipedia.org/wiki/Invariance of domain

Übersetzung von &#39linear invariance&#39 in Russisch