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!

Are x and ix linearly dependant or independant? (i=√-1)

  1. Oct 11, 2013 #1
    The question is: are x and ix linearly dependent or independent?

    My first guess is that they should be linearly dependent since i is a constant.

    But when you apply the definition of linear independence i.e. when you solve ax+ibx=0 (where x≠0), you get a=-ib which shows that the only solution can be a,b=0.

    Hence, according to definition of linear independence, x and ix should be linearly independent.

    Am I correct?
  2. jcsd
  3. Oct 11, 2013 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    I think you need to be claer about how you are setting up the vector space.
    i.e. In the complex plane, ix is perpendicular to x.

    Only if you insist that a and b are both real.
    The definition applies over a subset of a vector space - which vector space do these two numbers belong to?
  4. Oct 11, 2013 #3


    User Avatar
    Science Advisor

    In what vector space, with what field?

    Linear dependence has nothing to do with whether something is a constant.

    Why? ##b=2## and ##a=-2i## is also a solution.

    Consider the complex numbers as a one dimensional vector space over itself. What happens?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook