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:
“We must open our eyes and see that modern civilization has become so complex and the lives of civilized men so interwoven with the lives of other men in other countries as to make it impossible to be in this world and out of it.”
—Franklin D. Roosevelt (1882–1945)
“Who says that fictions only and false hair
Become a verse? Is there in truth no beauty?
Is all good structure in a winding stair?
May no lines pass, except they do their duty
Not to a true, but painted chair?”
—George Herbert (1593–1633)