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B Function and change of frame of reference

  1. Feb 14, 2017 #1
    Hello everybody,

    My question is about change of frame of reference and its consequences on an ordinary function.
    Let's ##B## a frame of reference that is linked to another one ##B'## through a change of basis matrix ##M##.
    So, for an equation written in the first basis ##B## as ##y=3x^2+2x-1##,
    what will be the corresponding writing (let ##y'=...##) in the second basis ##B'## by the use of matrix ##M## ?

    Thank you .

    Konte.
     
  2. jcsd
  3. Feb 14, 2017 #2

    FactChecker

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    Gold Member

    The function defines a mapping from one variable to another. Changing those variables to another frame of reference will not normally retain a well defined function. Translations will be ok, but a rotation will often make the function become multiple valued.
     
  4. Feb 14, 2017 #3

    mfb

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    2016 Award

    Staff: Mentor

    You can always express y and x in terms of y' and x', but in general you cannot solve the resulting equation for y'. You can still get an implicit function.
     
  5. Feb 15, 2017 #4
    Thank you guys for your answer.
     
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