Vectors, Matrices, and Arrays: Startup

Contents

Constructing Vectors

You can create a vertical vector by using semicolons:

VectorExample1 = [2; 4; 6; 1; 3; 5]
VectorExample1 =

     2
     4
     6
     1
     3
     5

which is a 6x1 size matrix. You can also choose to create a horizontal vector by using spaces or commas:

VectorExample2 = [2  4  6  1  3  5]
VectorExample3 = [2, 4, 6, 1, 3, 5]
VectorExample2 =

     2     4     6     1     3     5


VectorExample3 =

     2     4     6     1     3     5

which are both 1x6 size matrices.

Constructing Matrices and Arrays

Combine semicolons and commas/spaces, you can freely create NxM matrices or arrays:

MatrixExample1 = [2  4  6; 1  3  5]
MatrixExample2 = [2  4; 6  1; 3  5]
MatrixExample1 =

     2     4     6
     1     3     5


MatrixExample2 =

     2     4
     6     1
     3     5

Colon Operator

It is frequently useful to generate arrays of running indices by using the colon operator:

TryColon1 = [1:6]
TryColon2 = 1:6
TryColon1 =

     1     2     3     4     5     6


TryColon2 =

     1     2     3     4     5     6

A more general construction involves two colons, with the syntax (Starting Value) : (Increment) : (No Larger Than)

TryColon3 = 1:1:6
TryColon4 = 1:2:6
TryColon3 =

     1     2     3     4     5     6


TryColon4 =

     1     3     5

Here are some examples of more complicated arrays of running indices:

SampleArray1 = [2:2:6, 1:2:6]
SampleArray2 = [2:2:6; 1:2:6]
SampleArray1 =

     2     4     6     1     3     5


SampleArray2 =

     2     4     6
     1     3     5

Zero/Unit Arrays

It is considerably faster, less accident-prone, and much more convenient to predefine large arrays before using them. The functions zeros and ones work fantastic on defining arrays of zeros and ones:

ZeroArray = zeros(2,3)
OneArray = ones(2,3)
ZeroArray =

     0     0     0
     0     0     0


OneArray =

     1     1     1
     1     1     1

It also accepts the alternate syntax

Size = [2,3]
ZeroArray = zeros(Size)
Size =

     2     3


ZeroArray =

     0     0     0
     0     0     0

Exercise

Use colon operators to generate the following array:

A =

     1     2     3
     2     4     6
     3     6     9