Editing Linear complex structure (section)

{{Short description|Mathematics concept}}
In [[mathematics]], a [[Generalized complex structure|complex structure]] on a [[real vector space]] <math>V</math> is an [[automorphism]] of <math>V</math> that squares to the minus [[identity function|identity]], <math> - \text{id}_V </math>. Such a structure on <math>V</math> allows one to define multiplication by [[complex number|complex scalars]] in a canonical fashion so as to regard <math>V</math> as a [[complex vector space]].

Every complex vector space can be equipped with a compatible complex structure in a canonical way; however, there is in general no canonical complex 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 manifold]]s, by contrast to [[complex manifold]]s.  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'''.