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	Linear complex structure (en)
rdfs:comment	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)
sameAs	Linear complex structure Linear complex structure
dbp:wikiPageUsesTemplate	dbt:Math dbt:Short_description dbt:Isbn
Subject	Structures on manifolds
gold:hypernym	Automorphism
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Linear_complex_structure?oldid=1073304154&ns=0
Wikipage page ID	1549805 (xsd:integer)
page length (characters) of wiki page	16447 (xsd:nonNegativeInteger)
Wikipage revision ID	1073304154 (xsd:integer)
Link from a Wikipage to another Wikipage	Foundations of Differential Geometry Skew-Hermitian matrix Skew-symmetric matrix Algebra representation Algebraically closed field Almost complex manifold Antilinear map Associative algebra Automorphism Basis (linear algebra) Bilinear form Block matrix Structures on manifolds General linear group Generalized complex structure Dimension (vector space) Direct sum of modules Dual space Sesquilinear form Change of rings Definite form Digon Linear map Linear subspace Tensor algebra Complex conjugate Complex conjugate vector space Complex differential form Complex geometry Complex manifold Complex number Complexification Eigenvalues and eigenvectors Hermitian manifold Orthogonal transformation Composition operator Identity function If and only if Imaginary unit Symmetric algebra Symplectic matrix Symplectic vector space Diagonal matrix Exterior algebra Inner product space Transpose Vandermonde's identity Vector space Lie algebra Lie group Mathematics Multilinear form Multilinear map Real number Real structure Representation theory
has abstract	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)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Linear_complex_structure
is rdfs:seeAlso of	Linear form
is Wikipage redirect of	Complex linear structure Complex structure on a real vector space
is Link from a Wikipage to another Wikipage of	Algebra representation Almost complex manifold Cauchy–Riemann equations General linear group Generalized complex structure Hilbert transform Change of rings Linear form Complex conjugate vector space Complex manifold Complex number Complex structure Complexification Conway group Fubini–Study metric G-structure on a manifold Complex linear structure Complex structure on a real vector space
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Linear_complex_structure

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