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Math Help - Diagonalisable matrices

  1. #1
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    Diagonalisable matrices

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    How do I determine if this matrix is diagonalisable? Even with the hint im not sure, thanks..
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  2. #2
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    If x is in the range of M then x is an eigenvector (with eigenvalue 1). If x is in the kernel of M then x is an eigenvector (with eigenvalue 0). Now use the "rank plus nullity = n" theorem to conclude that the matrix has lots of eigenvectors.
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    Quote Originally Posted by qwerty1234 View Post
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    How do I determine if this matrix is diagonalisable? Even with the hint im not sure, thanks..

    Superhint: a square matrix is diagonalisable iff its minimal polynomial is the product of
    different linear factors.

    Tonio
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    ...and the problem explicitly gives you the minimal polynomial of M....
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