Editing MATLAB (section)

=== Vectors and matrices ===
A simple array is defined using the colon syntax: ''initial''<code>:</code>''increment''<code>:</code>''terminator''. For instance:
<syntaxhighlight lang="matlabsession">
>> array = 1:2:9
array =
 1 3 5 7 9
</syntaxhighlight>
defines a variable named <code>array</code> (or assigns a new value to an existing variable with the name <code>array</code>) which is an array consisting of the values 1, 3, 5, 7, and 9. That is, the array starts at 1 (the ''initial'' value), increments with each step from the previous value by 2 (the ''increment'' value), and stops once it reaches (or is about to exceed) 9 (the ''terminator'' value).

The ''increment'' value can actually be left out of this syntax (along with one of the colons), to use a default value of 1.
<syntaxhighlight lang="matlabsession">
>> ari = 1:5
ari =
 1 2 3 4 5
</syntaxhighlight>
assigns to the variable named <code>ari</code> an array with the values 1, 2, 3, 4, and 5, since the default value of 1 is used as the increment.

[[One-based indexing|Indexing]] is one-based,<ref>{{cite web|title=Matrix Indexing|url=http://www.mathworks.com/help/matlab/math/matrix-indexing.html|publisher=MathWorks|access-date=August 14, 2013}}</ref> which is the usual convention for [[matrix (mathematics)|matrices]] in mathematics, unlike zero-based indexing commonly used in other programming languages such as C, [[C++]], and [[Java (programming language)|Java]].

Matrices can be defined by separating the elements of a row with blank space or comma and using a semicolon to separate the rows. The list of elements should be surrounded by square brackets <code>[]</code>. Parentheses <code>()</code> are used to access elements and subarrays (they are also used to denote a function argument list).

<syntaxhighlight lang="matlabsession">
>> A = [16, 3, 2, 13  ; 5, 10, 11, 8 ; 9, 6, 7, 12 ; 4, 15, 14, 1]
A =
 16  3  2 13
  5 10 11  8
  9  6  7 12
  4 15 14  1

>> A(2,3)
ans =
 11
</syntaxhighlight>

Sets of indices can be specified by expressions such as <code>2:4</code>, which evaluates to <code>[2, 3, 4]</code>.  For example, a submatrix taken from rows 2 through 4 and columns 3 through 4 can be written as:
<syntaxhighlight lang="matlabsession">
>> A(2:4,3:4)
ans =
 11 8
 7 12
 14 1
</syntaxhighlight>
A square [[identity matrix]] of size ''n'' can be generated using the function <code>eye</code>, and matrices of any size with zeros or ones can be generated with the functions <code>zeros</code> and <code>ones</code>, respectively.
<syntaxhighlight lang="matlabsession">
>> eye(3,3)
ans =
 1 0 0
 0 1 0
 0 0 1

>> zeros(2,3)
ans =
 0 0 0
 0 0 0

>> ones(2,3)
ans =
 1 1 1
 1 1 1
</syntaxhighlight>

[[Transpose|Transposing]] a vector or a matrix is done either by the function <code>transpose</code> or by adding dot-prime after the matrix (without the dot, prime will perform [[conjugate transpose]] for complex arrays):
<syntaxhighlight lang="matlabsession">
>> A = [1 ; 2],  B = A.', C = transpose(A)
A =
     1
     2
B =
     1     2
C =
     1     2

>> D = [0, 3 ; 1, 5], D.'
D =
     0     3
     1     5
ans =
     0     1
     3     5
</syntaxhighlight>

Most functions accept arrays as input and operate element-wise on each element. For example, <code>mod(2*J,n)</code> will multiply every element in ''J'' by 2, and then reduce each element modulo ''n''. MATLAB does include standard <code>for</code> and <code>while</code> loops, but (as in other similar applications such as [[APL (programming language)|APL]] and [[R (programming language)|R]]), using the [[Array programming|vectorized]] notation is encouraged and is often faster to execute. The following code, excerpted from the function ''magic.m'', creates a [[magic square]] ''M'' for odd values of ''n'' (MATLAB function <code>meshgrid</code> is used here to generate square matrices {{mvar|I}} and {{mvar|J}} containing {{tmath|1:n}}):

<syntaxhighlight lang="matlab">
[J,I] = meshgrid(1:n);
A = mod(I + J - (n + 3) / 2, n);
B = mod(I + 2 * J - 2, n);
M = n * A + B + 1;
</syntaxhighlight>