Complex Vector
A complex vector is a vector whose members are complex numbers.
Contents
Description
A complex vector is simply a vector of complex numbers.
Properties
The double conjugate of a vector is the original vector: a̿ = a.
Conjugation is distributive.
Distance
Note that a complex vector as v = [1+i 1-i] would, according to the conventional definition for distance, have a magnitude of 0. Only the zero vector should have a magnitude of 0 however.
Distance of complex vectors relies on conjugation. Note that this is algebraically equivalent to calculating the distance of the absolute value. If v = a + bi = [a b], then the distance is ||v|| = √(a2 + b2).
In linear algebra notation, ||v|| = v̅Tv.