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# Vector Notation Question

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Hi guys, Would someone please clarify this for me: A function f: R3 -> R is Lipschitz if and only if there exists a -\ (greek lambda) such that |f(x) - f(y)| <= -\||x-y||. Alright, I understand everything except the difference between the | and the ||. I always understood ||v|| to be the length of v, but what the hell does the single | mean ? Thanks.

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|f(x) - f(y)| is the absolute difference of the function f evaluated at x and then at y.

TT

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It''s the same as ||(a,b)|| = sqrt(a^2+b^2) but |a| = sqrt(a^2), ie it''s just a one demensional distance function.

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The notation can also be used for complex numbers so:

|z| = |x+iy| = sqrt(x^2 + y^2)

and also matrices so:

|A| = det(A)

Although it''s not used all that often, it''s more frequent when writing the matrix out, then usually the curved brackets are left out and replaced with straight lines.

Some people also use it for the length of vectors as well, although all my lecturers tend to use the double lines.

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We just learned about vectors today in algebra and geometry, and my teacher was using |v| for a vector''s length, where v is a vector with an arrow written on top of it. Weird. :|

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