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01-Aug-1999 05:13 |
Comments
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non-linear?
by T. Lüttgert - Jun 20th 2002 04:21:54
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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Re: non-linear?
by Adrian Mariano - Jun 20th 2002 07:52:08
> 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.
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Re: non-linear?
by Eivind Magnus Hvidevold - Jun 14th 2005 04:30:09
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.
--
EMH
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