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Math Help - Finding a basis

  1. #1
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    Finding a basis

    Find basis for R3 relative to which the matrix for T is diagonal:

    T[x1, x 2, x3] = [-2x1 + x2 - x3, x1 - 2x2 - x3, -x1 - x2 - 2x3]
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  2. #2
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    Quote Originally Posted by chadlyter View Post
    Find basis for R3 relative to which the matrix for T is diagonal:

    T[x1, x 2, x3] = [-2x1 + x2 - x3, x1 - 2x2 - x3, -x1 - x2 - 2x3]
    Find the matrix T of the transformation.

    T=\begin{pmatrix} -2&1&-1 \\ 1&-2&-1 \\ -1&-1&-2 \end{pmatrix}

    Step 1 :
    find the eigenvalues

    Step 2 :
    find the eigenvectors associated to each eigenvalue

    Step 3 :
    it's done :P

    ---------------------------
    How to find eigenvalues :

    Find the characteristic polynomial, defined as :

    \chi_T(\lambda)=det(T-\lambda I_3)

    The eigenvalues will be the roots of the characteristic polynomial.
    ----------------------------

    Comment :
    Hmmm I have to check it out
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