Ronn! Blankenship wrote:
> At 05:34 PM Thursday 1/8/2009, Rceeberger wrote:
>> http://xkcd.com/526/
>>
>> xponent
>> Spit Goes Cunk Maru
>> rob
>
>
> I presume everybody here already knows that -40°C = -40°F.
>
>
> Linear Transformation Fixed Point Maru
Ronn!-- No, I didn't know that it was at -40.
But I did know there had to be one. I think
these are called "affine" transformations.
(Linear is x --> ax, and Affine is x --> ax + b.)
This usually works in any number of dimensions.
If x is a vector and A is an n by n matrix, then
the transformation is x --> Ax + b. We want
x = Ax + b, and solve:
Ix = Ax + b
(I-A)x = b
x = (I-A)^{-1} b.
That's unique, as long as A-I has an inverse.
It's a little simpler in 1 dimension, I guess...
---David
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