Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Normalising Imaginary Eigenvector

  1. Nov 3, 2015 #1
    Hello,

    whilst solving a system of coupled differential equations I came across an eigen vector of ##\vec{e_{1}} = (^{1}_{i})##.

    Assuming that this is a correct eigenvector, how do I normalise it? I want to say that ##\vec{e_{1}} = \frac{1}{\sqrt{2}} (^{1}_{i})## but if I sum ##1^{2} + i^{2}## I get zero.

    It seems sensible to me that the vector's length is root two, but how do I justify this, if at all?

    Thank you.
     
  2. jcsd
  3. Nov 3, 2015 #2

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    In a complex vector space, you have to introduce an inner product which satisfies ##\langle x, y\rangle = \overline{\langle y,x\rangle}##.
     
  4. Nov 3, 2015 #3
    The squared length of a complex vector v is defined by v.v(bar) where v(bar) is the complex conjugate, i believe. That will give you sqrt2
     
  5. Nov 4, 2015 #4
    Ah of course. A complex number is essentially a vector.

    Thank you.
     
  6. Nov 4, 2015 #5

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    I agree if you take away the "essentially". It is an element in a complex one-dimensional vector space. :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Normalising Imaginary Eigenvector
  1. Imaginary Numbers (Replies: 14)

  2. The imaginary Unit (Replies: 44)

  3. Imaginary volume (Replies: 1)

Loading...