10 Facts About Absolute value

For example, an absolute value is defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces.

The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts.

The term absolute value has been used in this sense from at least 1806 in French and 1857 in English.

Absolute value is thus always either a positive number or zero, but never negative.

Absolute value has the following four fundamental properties, that are used for generalization of this notion to other domains:.

The real absolute value function is a piecewise linear, convex function.

Real absolute value function has a derivative for every, but is not differentiable at.

Real absolute value function is an example of a continuous function that achieves a global minimum where the derivative does not exist.

Complex absolute value function is continuous everywhere but complex differentiable nowhere because it violates the Cauchy–Riemann equations.

Definition of absolute value given for real numbers above can be extended to any ordered ring.