|
Size: 664
Comment: Correction
|
Size: 1086
Comment: Distance
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 32: | Line 32: |
| Note that a complex vector as ''z = [1+i 1-i]'' would, according to the conventional definition for [[Calculus/Distance|distance]], have a magnitude of 0. Only the zero vector should have a magnitude of 0 however. Distance of complex vectors relies [[Calculus/ComplexNumbers#Complex_Conjugate|conjugation]]. In [[LinearAlgebra|linear algebra]] notation, the distance of complex vector ''z'' is equal to ''z̅^T^z''. |
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.
If c = ab, then c̅ = a̅b̅.
If c = a + b, then c̅ = a̅ + b̅.
If c = a - b, then c̅ = a̅ - b̅.
Distance
Note that a complex vector as z = [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 conjugation. In linear algebra notation, the distance of complex vector z is equal to z̅Tz.