About: Linear complex structure

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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.

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rdfs:label	Estructura compleja (es) Linear complex structure (en)
rdfs:comment	En matemáticas, una estructura compleja sobre un espacio vectorial real V es un automorfismo de V cuyo cuadrado es igual a menos la identidad en V. Tal estructura nos permitirá definir la multiplicación por escalares complejos de un modo canónico, permitiéndonos tratar así a V, que en un principio era solo un espacio vectorial real, como un espacio vectorial complejo. Las estructuras complejas tienen aplicación en representación de grupos y en , donde juegan un papel esencial en la definición de variedades casi complejas. (es) 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. (en)
dcterms:subject	Structures on manifolds
Wikipage page ID	1549805 (xsd:integer)
Wikipage revision ID	1073304154 (xsd:integer)
Link from a Wikipage to another Wikipage	Scalar matrix Multilinear map Hermitian form Representation theory Nondegenerate Basis (linear algebra) Bilinear form Definite bilinear form Algebra representation Almost complex manifold Lie group Structures on manifolds Complex conjugate vector space Complex number Complexification Mathematics Generalized complex structure Eigenspace Eigenvalue Function composition GL(n,C) Orthogonal transformation Lie algebra Complex differential form Complex geometry Complex manifold Automorphism Transpose Linear subspace Vandermonde's identity Dual space Extension of scalars Exterior algebra Foundations of Differential Geometry Complex conjugation Multilinear form Block matrix Symmetric algebra Real structure Associative algebra Real vector space Identity function If and only if Imaginary unit Inner product Inner product space Algebraically closed Real number Skew-symmetric matrix Tensor algebra Linear transformation Symplectic form Symplectic transformation Lie bracket Direct sum of vector spaces Block diagonal Skew-adjoint Conjugate-linear Hermitian structure Complex vector space Dimension (linear algebra)
sameAs	Linear complex structure Linear complex structure Linear complex structure Linear complex structure Linear complex structure
dbp:wikiPageUsesTemplate	dbt:Math dbt:Short_description dbt:Isbn
has abstract	En matemáticas, una estructura compleja sobre un espacio vectorial real V es un automorfismo de V cuyo cuadrado es igual a menos la identidad en V. Tal estructura nos permitirá definir la multiplicación por escalares complejos de un modo canónico, permitiéndonos tratar así a V, que en un principio era solo un espacio vectorial real, como un espacio vectorial complejo. Las estructuras complejas tienen aplicación en representación de grupos y en , donde juegan un papel esencial en la definición de variedades casi complejas. (es) 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. Every complex vector space can be equipped with a compatible complex structure, however, there is in general no canonical such structure. Complex structures have applications in representation theory as well as in complex geometry where they play an essential role in the definition of almost complex manifolds, by contrast to complex manifolds. The term "complex structure" often refers to this structure on manifolds; when it refers instead to a structure on vector spaces, it may be called a linear complex structure. (en)
gold:hypernym	Automorphism
prov:wasDerivedFrom	wikipedia-en:Linear_complex_structure?oldid=1073304154&ns=0
page length (characters) of wiki page	16447 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Linear_complex_structure
is rdfs:seeAlso of	Linear form Complex vector bundle
is Link from a Wikipage to another Wikipage of	Algebra representation Almost complex manifold Rizza manifold Complex number Complexification General linear group Generalized complex structure Orientifold

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