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:
“The money complex is the demonic, and the demonic is God’s ape; the money complex is therefore the heir to and substitute for the religious complex, an attempt to find God in things.”
—Norman O. Brown (b. 1913)
“When a house is tottering to its fall,
The strain lies heaviest on the weakest part,
One tiny crack throughout the structure spreads,
And its own weight soon brings it toppling down.”
—Ovid (Publius Ovidius Naso)