Inverse (mathematics)

Inversion (or finding the inverse) is an idea from mathematics, which is about finding a number, function or mathematical structure which is different from the current one, but which has similar properties. The simplest case of this is negation: Given a positive number, find the negative number which has the same value, except for the sign.

Inversion can refer to the following concepts:

• The inverse element for addition or for multiplication.
• An inverse function
• Inverse (logic)
• The inversion of an Invertible matrix
• The Fourier inversion theorem states that sometimes, it is possible to reconstruct the original function, after a Fourier transform
• In Set theory, the complement will return all elements not in the set.
• Inversive geometry studies the properties of a shape that are preserved after geometrical inversion.