Linear Complex 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.
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, and 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".
Read more about Linear Complex Structure: Definition and Properties, Compatibility With Other Structures, Relation To Complexifications, Extension To Related Vector Spaces
Famous quotes containing the words complex and/or structure:
“In ordinary speech the words perception and sensation tend to be used interchangeably, but the psychologist distinguishes. Sensations are the items of consciousness—a color, a weight, a texture—that we tend to think of as simple and single. Perceptions are complex affairs that embrace sensation together with other, associated or revived contents of the mind, including emotions.”
—Jacques Barzun (b. 1907)
“The syntactic component of a grammar must specify, for each sentence, a deep structure that determines its semantic interpretation and a surface structure that determines its phonetic interpretation.”
—Noam Chomsky (b. 1928)