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Additive Inverse


In an additive group G, the additive inverse of an element a is the element a^' such that a+a^'=a^'+a=0, where 0 is the additive identity of G. Usually, the additive inverse of a is denoted -a, as in the additive group of integers Z, of rationals Q, of real numbers R, and of complex numbers C, where -(x+iy)=-x-iy. The same notation with the minus sign is used to denote the additive inverse of a vector,

 v=(0,2,-3)==>-v=(0,-2,3),
(1)

of a polynomial,

 P(x)=x^4+2x^2-1==>-P(x)=-x^4-2x^2+1,
(2)

of a matrix

 A=[ 1.0 0.0; -4.0 1.5]==>-A=[-1.0  0.0; 4.0 -1.5],
(3)

and, in general, of any element in an abstract vector space or a module.


See also

Additive Group, Additive Identity, Multiplicative Inverse

This entry contributed by Margherita Barile

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Cite this as:

Barile, Margherita. "Additive Inverse." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/AdditiveInverse.html

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