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Math Help - Diagonalising a matrix with repeated eigenvalues

  1. #1
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    Diagonalising a matrix with repeated eigenvalues

    For further maths A level i was taught how to diag. a symmetric matrix. however the method of finding P as columns of the normalised eigenvectors only works if there are distinct eigenvals.
    However, if there are repeated what do u do?

    I've heard of the Gram Schmidt method but is there a simple method out there?
    How do i do the GS method if there's no other way
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  2. #2
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    If the matrix is symmetric then for each repeated eigenvalue (= root of the characteristic polynomial) there will be as many linearly independent eigenvectors for that eigenvalue as the multiplicity of the root. Choose an orthogonal set of such eigenvectors.
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