MatrixMultiplication

MatrixMultiplication - Matrix Multiplication A L TEX file:

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Unformatted text preview: Matrix Multiplication A L TEX file: matrixmultiplication-nb-all — Daniel A. Graham <daniel.graham@duke.edu>, June 22, 2005 Let p be the "row weights", q the "column weights" and A the matrix In: In: Out: p = {p1, p2} ; q = {q1, q2} ; A = {{a11, a12} , {a21, a22}} ; A//MatrixForm a11 a21 a12 a22 Premultiplying by p gives a list (vector) whose elements are the "weighted" averages of the rows of A: In: Out: p.A//MatrixForm a11 p1 + a21 p2 a12 p1 + a22 p2 Post multiplying by q gives a list (vector) whose elements are the "weighted" averages of the columns of A: In: Out: A.q//MatrixForm a11 q1 + a12 q2 a21 q1 + a22 q2 Doing both gives a scalar (number) representing the overall average when the rows are weighted by p and the columns by q: In: Out: Expand p .A.q a11 p1 q1 + a21 p2 q1 + a12 p1 q2 + a22 p2 q2 Page 1 of 1 ...
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