Thread: CauchySchwarz Inequality Help :D
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Old November 15th, 2008, 06:43 AM
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Hi,
Quote:
Originally Posted by brd_7 View Post
||x||=4, ||y||=5,<x,y>=8. (...)
What is the norm of 4x-4y?
\|4x-4y\|=4\|x-y\|=4\sqrt{\langle x-y,x-y\rangle}=4\sqrt{\langle x,x\rangle-2\langle x,y\rangle+\langle y,y\rangle}=\ldots
Quote:
What is the cosine angle between x and 4x-4y?
Remember that \langle u,v\rangle = \|u\|\|v\|\cos(u,v).
Quote:
Find λ, such that 2x-y and λx-y are orthogonal?
In other words, solve \langle 2x-y,\lambda x-y\rangle=0 for \lambda.
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