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Character (mathematics)
In mathematics, a character is (most commonly) a special kind of function from a group to a field (such as the complex numbers). There are at least two distinct, but overlapping meanings. Other uses of the word "character" are almost always qualified.
==Multiplicative character==
(詳細はgroup homomorphism from ''G'' to the multiplicative group of a field , usually the field of complex numbers. If ''G'' is any group, then the set Ch(''G'') of these morphisms forms an abelian group under pointwise multiplication.
This group is referred to as the character group of ''G''. Sometimes only ''unitary'' characters are considered (thus the image is in the unit circle); other such homomorphisms are then called ''quasi-characters''. Dirichlet characters can be seen as a special case of this definition.
Multiplicative characters are linearly independent, i.e. if are different characters on a group ''G'' then from it follows that .
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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