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September 23rd, 2010, 05:05 AM   #1
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2 unit vectors dot product

I need certain stopping criterion for approximating one unit vector with another. In case there is a perfect match (after a number of iterations), the dot product of the vectors is 1. I need to know (and have a reasoning for) whether in any other case the dot product of the original unit vector and the approximation (which is also a unit vector) is less than 1.
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September 23rd, 2010, 08:07 AM   #2
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Re: 2 unit vectors dot product

I presume that your vectors are in for some n and the dot product is the usual one on this space. In that case, remember that the dot product is given by where is the angle between u and v. In the case of two unit vectors, the dot product is just the cosine of the angle between them. What more, exactly, do you want to know?
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September 23rd, 2010, 08:48 AM   #3
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Re: 2 unit vectors dot product

That's all. I just need appropriate stopping criteria for the iterative procedure I implemented.
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