Other Examples
All the following examples are in fact abelian groups:
- addition of real valued functions: here, the additive inverse of a function f is the function −f defined by (−f )(x) = − f (x) , for all x, such that f + (−f ) = o , the zero function ( o(x) = 0 for all x ).
- more generally, what precedes applies to all functions with values in an abelian group ('zero' meaning then the identity element of this group):
- complex valued functions,
- vector space valued functions (not necessarily linear),
- sequences, matrices and nets are also special kinds of functions.
- In a vector space the additive inverse −v is often called the opposite vector of v. Additive inversion corresponds to scalar multiplication by −1. For Euclidean space, it is inversion in the origin.
- In modular arithmetic, the modular additive inverse of x is also defined: it is the number a such that a + x ≡ 0 (mod n). This additive inverse does always exist. For example, the inverse of 3 modulo 11 is 8 because it is the solution to 3 + x ≡ 0 (mod 11).
Read more about this topic: Additive Inverse
Famous quotes containing the word examples:
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold peoples attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (16881744)
Related Subjects
Related Phrases
Related Words