Lecture25

# Lecture25 - Algorithms in Systems Engineering IE170 Lecture...

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Algorithms in Systems Engineering IE170 Lecture 25 Dr. Ted Ralphs

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IE170 Lecture 25 1 References for Today’s Lecture Required reading CLRS Chapter 28
IE170 Lecture 25 2 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 . 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 . The set of all m × n matrices will be denoted R m × n .

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IE170 Lecture 25 3 Matrices The transpose of a matrix A is A T = a 11 a 21 ··· a m 1 a 12 a 22 ··· a
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## This note was uploaded on 02/29/2008 for the course IE 170 taught by Professor Ralphs during the Spring '07 term at Lehigh University .

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Lecture25 - Algorithms in Systems Engineering IE170 Lecture...

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