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lecture_4- Matrix Multiplication Part 2

lecture_4- Matrix Multiplication Part 2 - MA 265 LECTURE...

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MA 265 LECTURE NOTES: MONDAY, JANUARY 14 Matrix Multiplication Dot Product. Recall that a 2-vector or a 3-vector are matrices in the form bracketleftbigg x y bracketrightbigg or x y z , respectively. In general, we say that an n -vector is a matrix in the form x = x 1 x 2 . . . x n . The collection of all n -vectors will be denoted by R n . Define the dot product or inner product of two n -vectors as follows: a = a 1 a 2 . . . a n , b = b 1 b 2 . . . b n = a · b = a 1 b 1 + a 2 b 2 + · · · + a n b n . We can use shorthand notation to write this. Define summation notation as follows: x 1 + x 2 + · · · + x n = n summationdisplay k =1 x k . Hence the dot product is a = bracketleftbig a k bracketrightbig , b = bracketleftbig b k bracketrightbig = a · b = n summationdisplay k =1 a k b k . Example. Consider the following 4-vectors: u = 1 - 2 3 4 and v = 2 3 - 2 1 .
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