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etimología

Qué (quién) es linear complex - definición

MATHEMATICS CONCEPT

Complex conjugate linear map; Conjugate vector space; Conjugate linear map; Complex conjugate vector space

Line complex

3-DIMENSIONAL FAMILY OF LINES IN SPACE

Quadric line complex; Quadratic line complex; Linear complex

In algebraic geometry, a line complex is a 3-fold given by the intersection of the Grassmannian G(2, 4) (embedded in projective space P5 by Plücker coordinates) with a hypersurface. It is called a line complex because points of G(2, 4) correspond to lines in P3, so a line complex can be thought of as a 3-dimensional family of lines in P3.

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

Linear complex structure

COMPLEX STRUCTURE ON A REAL VECTOR SPACE V IS AN AUTOMORPHISM OF V THAT SQUARES TO THE MINUS IDENTITY

Complex structure on a real vector space; Complex linear structure

In mathematics, a complex structure on a real vector space V is an automorphism of V that squares to the minus identity, −I. Such a structure on V allows one to define multiplication by complex scalars in a canonical fashion so as to regard V as a complex vector space.

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

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)

Wikipedia

Complex conjugate of a vector space

In mathematics, the complex conjugate of a complex vector space $V\,$ is a complex vector space ${\overline {V}}$ , which has the same elements and additive group structure as $V,$ but whose scalar multiplication involves conjugation of the scalars. In other words, the scalar multiplication of ${\overline {V}}$ satisfies

where

*

is the scalar multiplication of

{\overline {V}}

and

\cdot

is the scalar multiplication of

V.

The letter

v

stands for a vector in

V,

\alpha

is a complex number, and

{\overline {\alpha }}

denotes the complex conjugate of

\alpha .

More concretely, the complex conjugate vector space is the same underlying real vector space (same set of points, same vector addition and real scalar multiplication) with the conjugate linear complex structure $J$ (different multiplication by $i$ ).

https://en.wikipedia.org/wiki/Complex conjugate of a vector space