updated definition: transformation

I've corrected and updated my Dictionary entry
for "transformation":
http://www.ixpres.com/interval/dict/transform.htm

I'd appreciate errata, criticism, etc.,
before I post an announcement on the big list.

In particular:

- is is correct to use the word "translation"?
(at the beginning of the definition)

- When I look at the final (bottom) diagram on the
"transformation" webpage (the one that has the d,q
unit-vectors divided into 1/7ths), my spatial imagination
tells me that the correct algebraic solution is:

x = (di + cj) / n
y = (bi + aj) / n

I can see by looking at the diagram that this is
the way the coordinates transpose according to the
matrix determinant, in a sort of criss-cross pattern.

But the formula I derive (about 1/5 of the way down
the page) is

x = (di - bj) / n
y = (aj - ci) / n

They're not the same. ... ?

Is the first set correct generally, or only for this
particular example? Or is it the second set that's
only correct in this particular example?

-monz

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