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Unformatted text preview: University of Toronto at Scarborough Department of Computer & Mathematical Sciences MAT A23 Winter 2008 Lecture 3 Sophie Chrysostomou Main ideas from lecture 2: 1. If v = [ v 1 , v 2 , ··· , v n ] , w = [ w 1 , w 2 , ··· , w n ] ∈ R n the dot product of v , w is defined to be the real number v · w = v 1 w 1 + v 2 w 2 + ··· + v n w n . 2. The angle, θ ∈ [0 , π ] between two nonzero vectors v and w in R n is given by θ = arccos parenleftbigg v · w bardbl v bardblbardbl w bardbl parenrightbigg . definition 0.1. We say that the vectors v , u ∈ R n are perpendicular or orthogonal ⇐⇒ v · u = 0 . We say that the magnitude of the vector v − u , bardbl v − u bardbl , is the distance between the vectors v − u Questions: 1) Does the definition for the angle between two angles in R n make sense? 2)What is a line, triangle, parallelogram, etc. in R n ? 1 example 0.2. Find the angle between the vectors v = [3 , 3 , , 0] and w = [1 , 4 , , − 1] Homework: 1. Show if u ∈...
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 Spring '10
 Sophie
 Linear Algebra, Algebra, Dot Product, Computer & Mathematical Sciences, Sophie Chrysostomou

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