1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
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
    2017 Award

    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
    2017 Award

    I agree if you take away the "essentially". It is an element in a complex one-dimensional vector space. :)
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook