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

Question on homogeneous systems

  1. Oct 10, 2009 #1
    Hello,
    how would you solve an homogeneous system of the form [itex]A\mathbf{x}=0[/itex], with the constrain [itex]<\mathbf{x},\mathbf{x}>=1[/itex]. The matrix A is symmetric, but I don't know if it matters.
    There should be a method involving eigenvalues, but strangely enough, I can't find it in any book.
    Thanks!
     
  2. jcsd
  3. Oct 10, 2009 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Why not just do the most straightforward thing? First solve Ax=0. Then among its solutions, solve <x,x>=0.
     
  4. Oct 10, 2009 #3
    The problem is that Ax=0 has a trivial solution which is x=0, and I am not interested in that.
     
  5. Oct 10, 2009 #4

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    If x=0 is entire solution set to Ax=0, then what does that say about the solution set to your original problem?
     
  6. Oct 10, 2009 #5
    actually I dont know if x=0 is the entire solution set for the system. Hopefully it is not. I am interested in figuring out whether there are other solutions or not. and eventually find them.
     
  7. Oct 10, 2009 #6

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Then do that -- use your linear algebra to find all of them.

    Then once you know all of them, you can find which of them satisfy your constraint.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Question on homogeneous systems
  1. Homogeneous system (Replies: 2)

Loading...