Matrices
Matrices on MatLab
An array is a collection of numbers or strings (text) and matrices are simply 2-dimentional arrays. Matlab 'understands' every parametre as a matrix. Even single numbers (e.g. x = 1) and vectors (e.g. v = [1 3 2]) are taken as 1-by-1 and (in this example) 1-by-3 matrices.
Creating Matrices
Entering matrices on Matlab is fairly easy. They are input by entering a list of numbers separated by commas (,) for elements on a same row and semi-colons (;) for elements on the next row.
As such, inputting:
A = [1, 2, 3; 4, 5, 6; 7, 8, 9];
B = [10, 11, 12; 13, 14, 15; 16, 17, 18];
Gives:
A =
1 2 3
4 5 6
7 8 9
B =
10 11 12
13 14 15
16 17 18
It is possible to concatenate matrices (link smaller matrices to make a bigger one) as such:
C = [A ; B];
Which gives:
C =
1 2 3
4 5 6
7 8 9
10 11 12
13 14 15
16 17 18
It is also possible to create matrices using the incremental notation seen earlier in order to save time by not having to write out each individual value:
D = [100: -11: 50; 45: -11: 0];
This gives a 2-by-5 matrix between 100 and 0 of increments -11:
D =
100 89 78 67 56
45 34 23 12   1
When creating matrices, further shortcuts include
The identity matrix
The zeroes matrix
The ones matrix
E = eye(3)
E =
1 0 0
0 1 0
0 0 1
F = zeroes(3)
F =
0 0 0
0 0 0
0 0 0
G = ones(3)
G =
1 1 1
1 1 1
1 1 1
Indexing
Consider the matrix:
A = [1, 2, 3; 4, 5, 6; 7, 8, 9];
Written as:
A =
1 2 3
4 5 6
7 8 9
1. Selecting the element in row 2 and column 3:
A(2,3)
Which returns:
ans =
6
2. Selecting the element in rows 1 to 2 and column 2 to 3:
A(1:2,2:3)
Which returns:
ans =
2 3
5 6
3. Selecting the first row:
A(1,:)
Which returns:
ans =
1 2 3
4. Selecting the third column:
A(:,3)
Which returns:
ans =
3
6
9
5. Selecting the element of index '4':
A(4)
Which returns:
ans =
2
N.B. MatLab indexes from 1 (not 0, unlike many other languages) and down each column. As such, in matrix A, the numbers 1, 4, 7 and 2 respectively have indices of 1, 2, 3 and 4. It is also possible of selecting multiple elements based on their indices using A(index_1, index_2, ..., index_n).