Double bar absolute value sign meaning?

Question

What do the double bars around in L[c]= Integral of ||C'(t)||dt from a to b when c is parametrized curve and L[c] is the length of c? Or just in general, what does it mean when there is a "double bar" absolute value sign? I'm aware it might have anything to do with abs. value. It's in the context of a differential geometry book.

Answer 1

It's the magnitude of a vector. For example, if you have v = = ai + bj, then ||v|| = √(a^2 + b^2), and if v = = ai + bj + ck, then v = √(a^2 + b^2 + c^2).



So if you have C(t) = x(t)i + y(t)j, then C'(t) = x'(t)i + y'(t)j, and ||C'(t)|| = √{[x'(t)]^2 + [y'(t)]^2}.

Answer 2

Double Absolute Value

Answer 3

Absolute Value Meaning

Answer 4

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RE:

Double bar absolute value sign meaning?

What do the double bars around in L[c]= Integral of ||C'(t)||dt from a to b when c is parametrized curve and L[c] is the length of c? Or just in general, what does it mean when there is a "double bar" absolute value sign? I'm aware it might have anything to do with abs. value....

Answer 5

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I believe it's the Euclidean norm. It is usually referring to vectors and it is defined as sqrt(u.u) where . is the inner (sometimes called Euclidean or dot) product. So as an example, if I have a vector v = [1, 2, 3] || v || = sqrt(v.v) = sqrt( (1*1)+(2*2)+(3*3) ) = sqrt( 1+4+9 ) = sqrt(15) ~ 3.87 Hope that makes sense to you :)