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Math Help - Finding the eigenvectors in a 3x3 matrix, given 3 eigenvalues!

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    Finding the eigenvectors in a 3x3 matrix, given 3 eigenvalues!

    A= the 3x3 matrix
    [0 1 0]
    [1 0 0]
    [0 0 3]
    I worked out the eigenvalues to be 1, -1, 3. How do i find the 3 eigenvectors, as i need them to find an orthogonal matrix. (because i am asked to orthogonally diagonalize this matrix).. Thanks in advance, help will be much appreciated, i have always been stuck on this, on finding eigen vectors in a 3x3 matrix!
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  2. #2
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    Quote Originally Posted by flawless View Post
    A= the 3x3 matrix
    [0 1 0]
    [1 0 0]
    [0 0 3]
    I worked out the eigenvalues to be 1, -1, 3. How do i find the 3 eigenvectors, as i need them to find an orthogonal matrix. (because i am asked to orthogonally diagonalize this matrix).. Thanks in advance, help will be much appreciated, i have always been stuck on this, on finding eigen vectors in a 3x3 matrix!
    Let x = [x_1,x_2,x_3]^T and \lambda denote eigenvalue.Use the definition:
    Ax = \lambda x

    So solve the following system of equations, three times, every time with a different \lambda, to get the three eigenvectors.
    x_2 = \lambda x_1
    x_1 = \lambda x_2
    3x_3 = \lambda x_3
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