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Unformatted text preview: Let u = ( u 1 , u 2 , ..., u n ) and v = ( v 1 , v 2 , ..., v n ) be vectors in R n . The dot product. u • v is defined to be: u • v = u 1 v 1 + u 2 v 2 + . . . + u n v n → → → → → → Sec 5.1 Saturday, February 06, 2010 11:13 PM Section5dot1 Page 1 Let u = ( u 1 , u 2 , ..., u n ) and v = ( v 1 , v 2 , ..., v n ) be vectors in R n . The dot product. u • v is defined to be: u • v = u 1 v 1 + u 2 v 2 + . . . + u n v n Also called the scalar product or the inner product of vectors. → → → → → → 5.1.1 Saturday, February 06, 2010 11:13 PM Section5dot1 Page 2 Let u = ( u 1 , u 2 , ..., u n ) and v = ( v 1 , v 2 , ..., v n ) be vectors in R n . The dot product. u • v is defined to be: u • v = u 1 v 1 + u 2 v 2 + . . . + u n v n Also called the scalar product or the inner product of vectors. → → → → → → u • v = 5 x 3 + 3 x 1 + 1 x (1) = 15 + 3  1 = 17 → → 5.1.2 Saturday, February 06, 2010 11:13 PM Section5dot1 Page 3 Let u = ( u 1 , u 2 , . . ., u n ) and v = ( v 1 , v 2 , ..., v n ) be vectors in R n . The dot product. u • v is defined to be: u • v = u 1 v 1 + u 2 v 2 + . . . + u n v n Also called the scalar product or the inner product of vectors. → → → → → → u • v = 5 x 3 + 3 x 1 + 1 x (1) = 15 + 3  1 = 17 → → u • v = 2 x (4) + 3 x (6) + (1) x 2 + 4 x 7 =  8  18  2 + 28 = 0 → → 5.1.3 Saturday, February 06, 2010 11:13 PM Section5dot1 Page 4 Let u = ( u 1 , u 2 , . . ., u n ) and v = ( v 1 , v 2 , ..., v n ) be vectors in R n . The dot product. u • v is defined to be: u • v = u 1 v 1 + u 2 v 2 + . . . + u n v n Also called the scalar product or the inner product of vectors. → → → → → → u • v = 5 x 3 + 3 x 1 + 1 x (1) = 15 + 3  1 = 17 → → u • v = 2 x (4) + 3 x (6) + (1) x 2 + 4 x 7 =  8  18  2 + 28 = 0 → → u • u = 5 x 5 + 3 x 4 + 1 x 1 = 5 2 + 3 2 + 1 2 = 25 + 9 + 1 = 35 → → * 5.1.4 Saturday, February 06, 2010 11:13 PM Section5dot1 Page 5 Let u = ( u 1 , u 2 , . . ., u n ) and v = ( v 1 , v 2 , ..., v n ) be vectors in R n . The dot product. u • v is defined to be: u • v = u 1 v 1 + u 2 v 2 + . . . + u n v n Also called the scalar product or the inner product of vectors. → → → → → → u • v = 5 x 3 + 3 x 1 + 1 x (1) = 15 + 3  1 = 17 → → u • v = 2 x (4) + 3 x (6) + (1) x 2 + 4 x 7 =  8  18  2 + 28 = 0 → → u • u = 5 x 5 + 3 x 4 + 1 x 1 = 5 2 + 3 2 + 1 2 = 25 + 9 + 1 = 35 → → *  u  = u 1 2 + u 2 2 + u 3 2 = 5 2 + 3 2 + 1 2 = 35 √ √ √...
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 Fall '07
 Tom
 Math, Linear Algebra, Algebra, Vectors, Dot Product, Orthogonal matrix, Saturday, Inner product space

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