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Math Help - Finding diagonalization of a matrix

  1. #1
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    Finding diagonalization of a matrix

    Thanks to all that can help. I'm given the matrix A= [-3, square root of 3] [ negative square root of 3, 1]. The question asks you to find the diagonalized matirx.

    I find the determinant to be A(A+2) where lamba=A so A1=0, A2=-2. Is this right? If it is what is my P matrix? I have only one eigenvector from A2=-2 to be [square root 3][1] and with that you can't get a P inverse. Which is needed for the formula D=P^1AP
    Last edited by nivek0078; September 25th 2012 at 06:20 AM.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Finding diagonalization of a matrix

    Quote Originally Posted by nivek0078 View Post
    I'm given the matrix A= [-3, square root of 3] [ negative square root of 3, 1]. I find the determinant to be A(A+2) where lamba=A so A1=0, A2=-2. Is this right?
    Right.

    If it is what is my P matrix? I have only one eigenvector from A2=-2 to be [square root 3][1] and with that you can't get a P inverse. Which is needed for the formula D=P^1AP
    Verify that a basis of V_0 is \{(1,\sqrt{3})\} and a basis of V_{-2} , \{(\sqrt{3},1)\} so, P=\begin{pmatrix} 1&\sqrt{3}\\\sqrt{3}&1\end{pmatrix} satisfies P^{-1}AP=\mbox{diag}(0,-2)
    Thanks from nivek0078
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  3. #3
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    Re: Finding diagonalization of a matrix

    Thank you FernandoRevilla for checking my work. I must have been over thinking it!
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