lecture27

lecture27 - IE170: Algorithms in Systems Engineering:...

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Unformatted text preview: IE170: Algorithms in Systems Engineering: Lecture 27 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University April 9, 2007 Jeff Linderoth (Lehigh University) IE170:Lecture 27 Lecture Notes 1 / 35 Taking Stock Last Time Easy Quiz This Time Numerical Linear Algebra Matrix representations Jeff Linderoth (Lehigh University) IE170:Lecture 27 Lecture Notes 2 / 35 Vectors and Matrices Vectors and matrices are constructs that arise naturally in many applications. Operating on vectors and matrices requires numerical algorithms. An m n matrix is an array of mn real numbers: A = a 11 a 12 a 1 n a 21 a 22 a 2 n . . . . . . . . . a m 1 a m 2 a mn A is said to have n columns and m rows . Jeff Linderoth (Lehigh University) IE170:Lecture 27 Lecture Notes 3 / 35 More Stuff You Know An n-dimensional column vector is a matrix with one column. An n-dimensional row vector is a matrix with one row . By default, a vector will be considered a column vector The set of all n-dimensional vectors will be denoted R n ....
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lecture27 - IE170: Algorithms in Systems Engineering:...

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