Function and change of frame of reference

[Konte]

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.

 

[FactChecker]

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.

 

[mfb]

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.

 

[Konte]

Thank you guys for your answer.