Function and change of frame of reference

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Discussion Overview

The discussion revolves around the implications of changing a frame of reference on a mathematical function, specifically how a function expressed in one basis relates to its expression in another basis through a change of basis matrix. The scope includes theoretical considerations and mathematical reasoning.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant questions how a function, such as ##y=3x^2+2x-1##, transforms when moving from frame of reference ##B## to ##B'## using a change of basis matrix ##M##.
  • Another participant suggests that changing variables to a different frame of reference may not retain a well-defined function, noting that translations are acceptable but rotations could lead to multiple-valued functions.
  • A further contribution indicates that while it is possible to express ##y## and ##x## in terms of ##y'## and ##x'##, the resulting equation for ##y'## may not be solvable, although an implicit function can still be derived.

Areas of Agreement / Disagreement

Participants express differing views on the effects of changing frames of reference, particularly regarding the retention of well-defined functions and the solvability of resulting equations. No consensus is reached on these points.

Contextual Notes

The discussion highlights potential limitations in defining functions across different frames, particularly concerning the nature of transformations (translations versus rotations) and the implications for function values.

Konte
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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.
 
Mathematics news on Phys.org
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.
 
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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.
 
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Thank you guys for your answer.
 

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