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 the case of all other sciences, arts, skills, and crafts, everyone is convinced that a complex and laborious programme of learning and practice is necessary for competence. Yet when it comes to philosophy, there seems to be a currently prevailing prejudice to the effect that, although not everyone who has eyes and fingers, and is given leather and last, is at once in a position to make shoes, everyone nevertheless immediately understands how to philosophize.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“If rightly made, a boat would be a sort of amphibious animal, a creature of two elements, related by one half its structure to some swift and shapely fish, and by the other to some strong-winged and graceful bird.”
—Henry David Thoreau (1817–1862)