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Representing a function in a different space

  1. Jun 21, 2011 #1
    I have an implicit function f(x,y,z) which represents a surface in the XYZ Cartesian reference frame. I would like to change this current XYZ reference frame by a matrix M.
    ie.
    [itex]M: XYZ \rightarrow X'Y'Z'[/itex]

    If I have a vector v in XYZ, then v'=Mv is my representation of v in the X'Y'Z' reference frame. But how do I get a representation of my function f in X'Y'Z'? Specially, as f is given in terms of (x,y,z) and cannot easily be solved for each of its components.

    Thanks
     
  2. jcsd
  3. Jun 22, 2011 #2
    f transforms as a scalar, that means (I put r = (x,y,z)):

    f(r) = f '(r ')

    and since r ' = Mr

    [itex]f'(r')=f(M^{-1}r')[/itex]

    In other words [itex]f'=f\circ M^{-1}[/itex]
     
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