Additive inverse

• 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; it has the same magnitude as the original and opposite direction. Additive inversion corresponds to scalar multiplication by −1. For Euclidean space, it is point reflection in the origin. Vectors in exactly opposite directions (multiplied to negative numbers) are sometimes referred to as antiparallel.
  • vector space-valued functions (not necessarily linear),
• 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 always exists. For example, the inverse of 3 modulo 11 is 8 because it is the solution to 3 + x ≡ 0 (mod 11).

Non-examples

Natural numbers, cardinal numbers and ordinal numbers do not have additive inverses within their respective sets. Thus one can say, for example, that natural numbers do have additive inverses, but because these additive inverses are not themselves natural numbers, the set of natural numbers is not closed under taking additive inverses.

See also

• −1
• Absolute value (related through the identity |−x| = |x|).
• Additive identity
• Inverse function
• Involution (mathematics)
• Multiplicative inverse
• Reflection symmetry
• Semigroup
• Monoid
• Group (mathematics)