lec5_1

# lec5_1 - turn out to be fundamental and the good starting...

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NOTES ON SECTION 4 . 2 MA265, SECTIONS 41, 52 Some key words 1. Inner Product in R 2 , R 3 You will certainly already know this material (if you really don’t, you’ll easily get up to speed in this section). There are really two main points to make: (1) The dot product determines notions of distance: || x - y || = p ( x - y ) · ( x - y ). (2) It also determines notions of angle between two vectors x , y : cos( θ ) = x · y || x |||| y || We will note also the following Theorem, not because it is diﬃcult but because these properties
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Unformatted text preview: turn out to be fundamental and the good starting point for a very useful abstraction: Theorem 1. The following identities hold for all choices of u , v , w and c ∈ R : (a) u · u ≥ , and is equal to zero if and only if u = . (b) u · v = v · u (c) ( u + v ) · w = u · w + v · w (d) ( c u ) · v = c ( u · v ) 1...
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