Presentation2 - Vectorsandmatrices Avector .Wehavecolumn...

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Vectors and matrices
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A vector Order collec2on of numbers. We have column or row vectors. Vectors of coordinates a = 5 2 3 a t = (5,2, 3) b = 4 2 b t = (4,2) x y z (x 1 ,y 1 ,z 1 )
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Adding vectors c=a+b a = 1,0 ( ) b = 6,2 ( ) c = a + b = 1,0 ( ) + ( ) = 1 + 6,0 + 2 ( ) = 7,2 ( )
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Products of vectors Scalar of inner products are deFned as (must be of the same length ) The length of a vector is given by the square root of the inner product of the vector by self l = a i * a i i a = a 1 , a 2 ,..., a n ( ) b = b 1 , b 2 ,..., b n ( ) a t * b = a i * b i i = 1,. .., n
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Matrices Like vectors, set of ordered numbers, now with two indices (Frst for rows, second for columns). We denote matrices with CAPS. Matrix mul2plica2on is deFned as (the number of columns of A must be the same as the number of rows in B). The result is a matrix A = 1 5 7 2 4 14 8 9 1 2 4 7 5 25 3 3 A 23 = 8 C ij = A ik B kj k
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Adding matrices (example) A=A+B A = 3 6 2 1 B = 0 2 5 8 C = A + B = 3 6 2 1 + 0 2 5 8 C = 3 + 0 6 2 2 +
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Presentation2 - Vectorsandmatrices Avector .Wehavecolumn...

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