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If L is a subcollection of a simplicial complex K that contains all faces of its elements, then L is another simplicial complex called a simplicial subcomplex.

A complex map is a map f:C->C. The following table lists several common types of complex maps. map formula domain complex magnification f(z)=az a in R, a>0 complex rotation ...

A Kähler structure on a complex manifold M combines a Riemannian metric on the underlying real manifold with the complex structure. Such a structure brings together geometry ...

A matrix whose elements may contain complex numbers. The matrix product of two 2×2 complex matrices is given by (1) where R_(11) = ...

A doubly periodic function with periods 2omega_1 and 2omega_2 such that f(z+2omega_1)=f(z+2omega_2)=f(z), (1) which is analytic and has no singularities except for poles in ...

The complex plane is the plane of complex numbers spanned by the vectors 1 and i, where i is the imaginary number. Every complex number corresponds to a unique point in the ...

The fundamental theorem of arithmetic states that every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of ...

A field K is said to be an extension field (or field extension, or extension), denoted K/F, of a field F if F is a subfield of K. For example, the complex numbers are an ...

The extended complex plane is the name given to the complex plane with a point at infinity attached: C union {infty^~}, where infty^~ denotes complex infinity. It is also ...

Let omega be the cube root of unity (-1+isqrt(3))/2. Then the Eisenstein primes are Eisenstein integers, i.e., numbers of the form a+bomega for a and b integers, such that ...