3.3: Vectors and Arrays in MFile Environments
One significant capability of environments accounts for much of their popularity among engineers: their ability to do vector and matrix computations. Mfile environments can operate on the following types of values:
 Scalar  a scalar is a single value (i.e. a number).
 Vector  a vector is an ordered series of numbers.
 Matrix  a matrix is a rectangular array of numbers.
 String  variables may also contain strings of characters.
Note: The ability to do computations on vectors and matrices gives MATLAB its name (MATrix LABoratory).
Vector Basics
There are several ways to create a vector of values. One is to enclose the values in square brackets. For example, the command
[9 7 5 3 1]
creates the vector of values 9, 7, 5, 3, and 1. This vector can be assigned to a variable
v
:
>> v = [9 7 5 3 1]
v =

9 7 5 3 1
A second way to create a vector of values is with the sequence notation
start:end
or
start:inc:end
.
For example,
1:10
creates the vector of integers from 1 to 10:
>> 1:10
ans =

1 2 3 4 5 6 7 8 9 10
The command
1:0.1:2
creates the vector
>> 1:0.1:2
ans =

1.0000 1.1000 1.2000 1.3000 1.4000 1.5000 1.6000 1.7000 1.8000 1.9000 2.0000
The command
10:1:1
creates the vector
>> 10:1:1
ans =

10 9 8 7 6 5 4 3 2 1
Vector elements are accessed using numbers in parentheses. For example if the vector
v
is defined as
v = [9 7 5 3 1]
, the second element of
v
can be accessed as
>> v(2)

ans = 7
The fourth element of
v
can be changed as follows:
>> v(4) = 100
v =

9 7 5 100 1
Element by Element Operations on Vectors
In addition to vector and matrix arithmetic, many operations can be performed on each element of the vector. The following examples use the vector
v = [9 7 5 3 1]
and
the scalar value
val
which is 5 in the examples.
Addition: the command
v+val
adds
val
to each element of
v
:
>> v+5
ans =

14 12 10 8 6
Subtraction: the command
vval
subtracts
val
from each element of
v
:
>> v5
ans =

4 2 0 2 4
Multiplication: the command
v*val
multiplies each element of
v
by
val
:
>> v*5
ans =

45 35 25 15 5
Division: the command
v/val
divides each element of
v
by
val
:
>> v/5
ans =

1.80000 1.40000 1.00000 0.60000 0.20000
The command
val./v
divides
val
by
each element of
v
:
>> 5./v
ans =

0.55556 0.71429 1.00000 1.66667 5.00000
Exponentiation: the command
v.^val
raises each element of
v
to the
val
th power:
>> v.^2
ans =

81 49 25 9 1
More Information on Vectors and Matrices
An excellent tutorial on how to use MATLAB's vector and array capabilities is at the Mathworks MATLAB tutorial page http://www.mathworks.com/academia/student_center/tutorials/performing_calculations.html
One useful method of accessing entire rows or entire columns of the matrix is not mentioned in the tutorial. Suppose that the matrix
A
is defined as
\begin{align*}\begin{matrix} >> A = & [1 & 2 & 3 & 4 & 5\\ & 6 & 7 & 8 & 9 & 10\\ & 11 & 12 & 13 & 14 & 15\\ & 16 & 17 & 18 & 19 & 20] \end{matrix}\end{align*}
\begin{align*}\begin{matrix} A = & 1 & 2 & 3 & 4 & 5\\ & 6 & 7 & 8 & 9 & 10\\ & 11 & 12 & 13 & 14 & 15\\ & 16 & 17 & 18 & 19 & 20 \end{matrix}\end{align*}
An entire row of
A
can be obtained by specifying a single ":" as the column index:
>> A(2,:)
ans =

6 7 8 9 10
Similarly, an entire column of
A
can be obtained by specifying a single ":" as the row index:
>> A(:,3)
\begin{align*}\begin{matrix} \text{ans} =\\ &3\\ &8\\ &13\\ &18 \end{matrix}\end{align*}
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