A linear function is of the form f(x) = ax + b, while a linear transformation satisfies T(a + b) = T(a) + T(b). So the "function" is linear, but the "transformation" is not. Of course, the function and the transformation is the same, so it depends on the context which one applies. A transformation is obviously what the units developers had in mind, and that is probably natural given that units are transformed to other units.
> Fahrenheit <-> Celsius is a
> perfectly linear conversion:
> T[C] = (T[F]-32)/1.8
No, it is an affine transformation, not a linear one because of the constant offset. If F is a linear transformation then it must satisfy the property F(a+b)=F(a)+F(b). This is clearly false for the above temperature conversion. For example 32 degrees Fahrenheit is 0 degrees Celsius but 32+32=64 degrees Fahrenheit is not 0+0=0 degrees Celsius.
Maybe this is nit-picking, but Fahrenheit <-> Celsius is a perfectly linear conversion:
T[C] = (T[F]-32)/1.8
non-linear would be Energy to Wavelength, for example.
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