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Math Help - Eigenvectors

  1. #1
    Junior Member
    Joined
    Nov 2007
    Posts
    27

    Eigenvectors

    Does anyone know how to:
    Show that the matrix B=

    [php]
    -4 1 0 . . 0 1
    1 -4 1 0 . . 0
    0 1 -4 1 .. . .
    : : : : 0
    0 . . 0 1 -4 1
    1 0 . . 0 1 -4
    [/php]


    has v=
    [php]
    1
    1
    1
    .
    :
    1
    1
    [/php]
    as an eigenvector.
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  2. #2
    Member
    Joined
    May 2006
    Posts
    244
    Quote Originally Posted by smiler View Post
    Does anyone know how to:
    Show that the matrix B=

    [php]
    -4 1 0 . . 0 1
    1 -4 1 0 . . 0
    0 1 -4 1 .. . .
    : : : : 0
    0 . . 0 1 -4 1
    1 0 . . 0 1 -4
    [/php]


    has v=
    [php]
    1
    1
    1
    .
    :
    1
    1
    [/php]
    as an eigenvector.
    As every row of the matrix has three non-zero elements 1,1,-4 every element of the matrix times your vector is -2, and so your vector is an eigen-vector of the matrix corresponding to e-value -2.

    ZB
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