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Math Help - Diagonalizable matrix

  1. #1
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    Diagonalizable matrix

    Are the following matrices diagonalizable:





    I think neither are diagonalizable because they don't have at least two linearly independent eigenvectors. Am I correct?
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    MHF Contributor harish21's Avatar
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    Quote Originally Posted by temaire View Post
    Are the following matrices diagonalizable:





    I think neither are diagonalizable because they don't have at least two linearly independent eigenvectors. Am I correct?
    To diagonalize a matrix, I would first find the eigenvectors. The three eigenvectors v_1, v_2, v_3 will form the three columns(c1,c2,c3) of the matrix P.

    If P is invertible , then the matrix given by P^{-1} A P = D is the diagonal matrix
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    Quote Originally Posted by harish21 View Post
    To diagonalize a matrix, I would first find the eigenvectors. The three eigenvectors v_1, v_2, v_3 will form the three columns(c1,c2,c3) of the matrix P.

    If P is invertible , then the matrix given by P^{-1} A P = D is the diagonal matrix
    I have found the eigenvectors for both matrices. However, I only found one eigenvector for each matrix, which means that the two matrices do not have at least two linearly independent eigenvectors, which means that they are not diagonalizable. Is this correct?
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  4. #4
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by temaire View Post
    I have found the eigenvectors for both matrices. However, I only found one eigenvector for each matrix, which means that the two matrices do not have at least two linearly independent eigenvectors, which means that they are not diagonalizable. Is this correct?

    A n \times n matrix is diagonalizable only if it has n linearly independent eigenvectors.

    So your matrix is not diagonalizable!
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