# Submatrices

Start by defining a matrix

A = [1 2 3; 4 5 6; 7 8 9; 10 11 12]

A = 1 2 3 4 5 6 7 8 9 10 11 12

The dimensions of a matrix are given by

[r c] = size(A)

r = 4 c = 3

We can use this to define a new matrix

B = ones(size(A))

B = 1 1 1 1 1 1 1 1 1 1 1 1

Note: **Indexing in MATLAB always begins with 1**

To access a single element of type

A(2,3)

ans = 6

The second column of is given by

A(:,2)

ans = 2 5 8 11

The third row of is given by

A(3,:)

ans = 7 8 9

Here's a submatrix (the second and third rows of the first three columns)

A(2:3,1:3)

ans = 4 5 6 7 8 9

We can replace parts of a matrix

B(2,:) = [2 4 6]

B = 1 1 1 2 4 6 1 1 1 1 1 1

or

A(1:2,1:2) = B(2:3,2:3)

A = 4 6 3 1 1 6 7 8 9 10 11 12

We can also easily remove certain rows or columns of a matrix by assigning an empty vector '[]':

A([2 4],:) = []

A = 4 6 3 7 8 9