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Math Help - Diagonalisation of Matrices..

  1. #1
    Junior Member
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    Diagonalisation of Matrices..

    Ok

    So i am understanding that any M matrix can be rewritten such that M= UDU^-1, where U consists of the matrix consisting of the eigenvectors and D is the diagonal matrix consisting of eigenvalues.

    Is there another way to think about this idea through transformations?
    i.e

    1. How does the matrix U relate to the matrix M in terms of transformations? Are they related in any way?
    2. The matrix D is clearly the enlargement with the scale factors of eigenvalues in x & y directions?.So is it possible to think of the matrix M as a series of three transformation and can someone give me an example where all this makes sense?

    Fundamentally, i want to understand why a matrix can be broken up in this way?

    Also, and other than the idea of powers is there another application of this result?
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  2. #2
    MHF Contributor
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    Re: Diagonalisation of Matrices..

    Hey rodders.

    You want to look at rotation groups and algebras that deal with this specific AXA^(-1)
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  3. #3
    Junior Member
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    Re: Diagonalisation of Matrices..

    Thanks! More reading required then!
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