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!

Pruning a set of matrices (easy)

  1. May 19, 2012 #1
    http://dl.dropbox.com/u/33103477/prune.png [Broken]

    I am unsure if the the answer is:

    [tex] {\begin{pmatrix}
    2 & 1 \\
    5 & 1
    \end{pmatrix}},
    {\begin{pmatrix}
    3 & -1 \\
    7 & 4
    \end{pmatrix}} [/tex]

    or

    [tex] {\begin{pmatrix}
    2 & 1 \\
    5 & 1
    \end{pmatrix}},
    {\begin{pmatrix}
    3 & -1 \\
    7 & 4
    \end{pmatrix}},
    {\begin{pmatrix}
    2 & 7 \\
    -4 & 1
    \end{pmatrix}} [/tex]

    I'm pretty sure it's the second one but am a bit confused about when the algorithm stops.
    Can someone confirm the answer ?
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. May 19, 2012 #2
    I have never encountered the word prune, but by context, I believe it is saying X is linearly dependent and you want to make a set Y (lin ind) from X that spans ##M_{2,2}## as well.

    If that is the case, you just need to verify that none of the matrices in your 3 set are linearly dependent to the other two. If that is the case, then the 3 matrix set is correct.
     
    Last edited by a moderator: May 6, 2017
  4. May 19, 2012 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Lay them out as 4-dimensional vectors, then look for a subset that generates the whole span. In other words, start with the vectors
    [tex] \begin{array}{l}v_1 = [2,1,5,1] \\v_2 = [3,-1,7,4] \\ v_3 = [5,-5,11,10] \\
    v_4 = [2,7 -4,1]\end{array}[/tex] Obviously, [itex] v_1, v_2[/itex] are linearly independent.
    Are the three vectors [itex] v_1, v_2, v_3[/itex] linearly independent? If not, [itex]v_3[/itex] is in the span of [itex] v_1, v_2.[/itex] If they are linearly independent, throw in [itex] v_4[/itex] and continue the test.

    Note: you can do it all in one step, just by doing row operations on the 4x4 matrix with rows v_i. Basically, you are looking for solutions of the 4x4 linear system [itex] c_1 v_1 + c_2 v_2 + c_3 v_3 + c_4 v_4 = 0.[/itex]

    RGV
     
    Last edited by a moderator: May 6, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Pruning a set of matrices (easy)
Loading...