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DM559 Linear and Integer Programming Lecture 3 Matrix Operations Marco Chiarandini Department of Mathematics & Computer Science University of Southern Denmark Matrices Vectors Vectors and Matrices Outline More on Linear Systems 1. Matrices 2. Vectors 3. Vectors and Matrices 4. More on Linear Systems 2 Matrices Vectors Vectors and Matrices Outline More on Linear Systems 1. Matrices 2. Vectors 3. Vectors and Matrices 4. More on Linear Systems 3 Matrices Vectors Vectors and Matrices Matrices More on Linear Systems Definition (Matrix) Amatrix is a rectangular array of numbers or symbols. It can be written as a11 a12 ··· a1n a21 a22 ··· a2n . . . . . . .. . . . . a a · · · a m1 m2 mn • We denote this array by a single letter A or by (aij) and • we say that A has m rows and n columns, or that it is an m × n matrix. • The size of A is m × n. • The number a is called the (i,j) entry or scalar. ij 4
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