A transformation is conformal, or angle-preserving, if at every point the Jacobian is a scalar times an orthogonal matrix; this means that if J is the Jacobian, then JJT = kI. Computing the Jacobian in the case zi = xi/||x||^2, where ||x||^2 = x12+...+xn2 gives JJT=kI, with k = 1/||x||^4; hence.......what?
Goddess Artemis! Slain thy enemies.....
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Fate: Protects fools, little children and ships named Enterprise...
Fate: Also beats the merry hell out of the Battlestar Galactica.
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House Quote of the Day!
"I was curious. But since I'm not a cat, that's not dangerous to me." Dr House MD
I don't think that metaphor was actually designed to warn cats.
Dr Wilson MD (Just)
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