lec1_3

lec1_3 - NOTES ON SECTION 1 3 MA265 Key words Dot product...

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Unformatted text preview: NOTES ON SECTION 1 . 3 MA265, SECTIONS 41, 52 Key words Dot product Coefficient matrix inner dimensions Matrix product augmented matrix Given two n-vectors (they have to be the same size), the dot product is defined as the obvious general- ization of this example: [1 ,- 4 , 2 ,π ] · 1 2 1 2 = 1 * (1) + (- 4) * 2 + 2 * 1 + π * 2 =- 5 + 2 π Given two matrices A = a 11 a 12 ... a 1 n a 21 a 22 ... a 2 n a 31 a 32 ... a 3 n . . . . . . . . . a m 1 a m 2 ... a mn ,b = b 11 b 12 ... b 1 p b 21 b 22 ... b 2 p b 31 b 32 ... b 3 p . . . . . . . . . b n 1 b m 2 ... b np the matrix product A * B is the matrix with i,j-entry equal to n X k =1 a i,k * b k,j i.e. it is the “dot product” 1 of the i th row of A and the j th column of B . It only makes sense if the inner dimensions are equal: A = m × n and B = n × p , and the product makes sense because “...
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This note was uploaded on 03/31/2012 for the course MA 265 taught by Professor Bens during the Spring '08 term at Purdue.

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lec1_3 - NOTES ON SECTION 1 3 MA265 Key words Dot product...

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