Absolute value has a different meaning in the case of complex numbers: for a complex number , the absolute value of is defined to be , where and are real.
All absolute value functions satisfy the defining properties of a valuation, including:
for all , with equality if and only if
for all (triangle inequality)
However, in general they are not literally valuations, because valuations are required to be real valued. In the case of and , the absolute value is a valuation, and it induces a metric in the usual way, with distance function defined by .
|Date of creation||2013-03-22 11:52:09|
|Last modified on||2013-03-22 11:52:09|
|Last modified by||djao (24)|