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

I Question On Linear Independence

  1. Nov 2, 2016 #1
    We were going over linear independents in class and my professor said that if y1 and y2 are linearly independent then the ratio of y2/y1 is not a constant, but he never explained why it is not a constant.
     
  2. jcsd
  3. Nov 2, 2016 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hi,
    You can turn it around: if y1 and y2 are linearly dependent, there is a ##\lambda## such that ##y_1 = \lambda y_2##
     
  4. Nov 2, 2016 #3

    Krylov

    User Avatar
    Science Advisor
    Education Advisor

    Given that you posted this in a differential equations subforum, I take it that ##y_1## and ##y_2## belong to some vector space of functions that contains the solutions of a certain linear differential equation?

    Provided this is indeed your setting, what (by definition) does it mean when ##y_{1,2}## are independent? What does it mean when they are dependent?
     
  5. Nov 2, 2016 #4

    Mark44

    Staff: Mentor

    Minor point -- you were going over linear independence in class. Linear independence is an attribute of a set of vectors of other elements that belong to a vector space.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Question On Linear Independence
  1. Linear Independence (Replies: 8)

Loading...