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Math Help - [SOLVED] linear transformation question

  1. #1
    tricky hornet
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    Post [SOLVED] linear transformation question

    can anyone tell me this, it's driving me crazy because it should be easy. here goes.
    For a roation of the vector (x,y,z) ( in 3-space obviously) about an axis which is determined by an arbitrary unit vector U=(a,b,c) through a positive angle beta(@), prove that that transformation Matrix is defined as

    [HTML] a^2(1-cos@)+cos@ ab(1-cos@)-csin@ ac(1-cos@)+bsin@

    ab(1-cos@)+csin@ b^2(1-cos@)+cos@ bc(1-cos@)-asin@

    ac(1-cos@)-bsin@ bc(1-cos@)+asin@ c^2(1-cos@)+cos@ [/HTML]
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  2. #2
    Super Member Rebesques's Avatar
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    what?

    I tried a little net search, and came up with

    http://mathworld.wolfram.com/RotationFormula.html

    I put n=U and r=(x,y,z), and after some brief computations, formula (3) of that page is exactly r'=Ar, where A is the matrix given.

    Tell me if the derivation of the formula seems difficult (...not that I will be able to help :P)

    Last edited by Rebesques; July 27th 2005 at 02:06 AM.
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