Engineering Optimization: Theory and Practice, Fourth Edition

792 Introduction to MATLAB

C.2 Defining Matrices in MATLAB

Before performing arithmetic operations or using them in developing MATLAB pro-

grams or m-files, the relevant matrices need to be defined using statements such as the

following.

1.A row vector or 1×nmatrix, denotedA, can be defined by enclosing its

elements in brackets and separated by either spaces or commas.

Example: A=[1 2 3]

2.A column vector orn×1 matrix, denotedA, can be defined by entering its

elements in different lines or in a single line using a semicolon to separate them

or in a single line using a row vector with a prime on the right-side bracket (to

denote the transpose).

Example: [1

A= 2 , A=[1; 2 ; 3],orA=[1 2 3]′.

3 ]

3.A matrix of sizem×n, denotedA, can be defined as follows (similar to the

procedure used for a column vector).

Example: [1 2 3

A=4 5 6 ,orA=[1 2 3; 4 5 6; 7 8 9].

7 8 9]

4.Definitions of some special matrices:

A=eye( 3 )

implies an identity matrix of order 3: A=





1 0 0

0 1 0

0 0 1



.

A=ones( 3 )

implies a square matrix of order 3 with all elements equal to one:A=





1 1 1

1 1 1

1 1 1



.

A=zeros( 2 , 3 )

implies a 2×3matrix with all elements equal to zero: A=

[

0 0 0

0 0 0

]

.

5.Some uses of the colon operator (:):

(i) To generate all numbers between 100 and 50 in increments of− 7

> >100 :−7 : 50

This command generates the numbers 100 93 86 79 65 58 51