1. Not finding help here? Sign up for a free 30min 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!

Finding basis for an eigenspace

  1. Nov 20, 2008 #1
    1. The problem statement, all variables and given/known data
    Find a basis and dimension for each eigenspace of the matrix:

    4 2
    3 3

    2. Relevant equations

    3. The attempt at a solution
    I found the eigenvalues lambda = 1, 6. When trying to find the eigenspace for lambda = 1, I try to solve for x and y here:

    |-3 -2| |x| = |0|
    |-3 -2| |y| = |0|

    I'm not sure how to do the matrix notation on here but I hope it is clear enough. Since I get the same equation twice in the system of equations, is this the right basis: span(-2/3, 1)?

    edit: can someone also see if I did the basis for the 2nd eigenvalue (lambda = 6) correctly? I get the basis to be span(1, 1).
    So each has dimension of 1
  2. jcsd
  3. Nov 20, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Um, yes. If I'm reading your notation correctly, you have the right eigenspace for both. Is this a question, or just a homework check?
  4. Nov 20, 2008 #3
    It was originally going to be a question but I kind of figured it out as I was typing it :)
    So I was just making sure.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Finding basis for an eigenspace
  1. Basis of eigenspace (Replies: 3)