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Math Help - find the eigenspace

  1. #1
    Senior Member
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    Jan 2010
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    find the eigenspace

    I have subin the eigenvalue then I got the matrix

    [0 1 3 1]
    [0 1 2 4]
    [0 0 2 2]
    [0 0 1 3]
    reduce to

    [0 1 0 -8]
    [0 1 0 2]
    [0 0 2 2]
    [0 0 1 3] does this imply x3 = x4 =0? what is x1 then, how do I write it in terms of t and s?
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  2. #2
    Banned
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    Quote Originally Posted by wopashui View Post
    I have subin the eigenvalue then I got the matrix

    [0 1 3 1]
    [0 1 2 4]
    [0 0 2 2]
    [0 0 1 3]
    reduce to

    [0 1 0 -8]
    [0 1 0 2]
    [0 0 2 2]
    [0 0 1 3] does this imply x3 = x4 =0? what is x1 then, how do I write it in terms of t and s?

    You have "subin"...?? Anyway, if the last matrix is the reduced one to find the eigenspace of whatever, then indeed the 3rd and 4th rows imply that x_3=x_4=0 , and the 2nd row then implies x_2=0 as well...and x_1 can be freely chosen , so in this case the subspace (eigenspace or whatever) is \left\{\begin{pmatrix}x\\0\\0\\0\end{pmatrix}\,,\,  \,any\,\,\,x\right\}.

    Tonio
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