The main data structures in MATLAB are vectors and matrices. If you have never heard of these before, then look them up in:
before you continue.
Vectors in MATLAB are $n\times 1$ or $1\times n$ arrays of numbers.
Suppose the vector $u$ is given by $u=(1\;4\;9)$. This may be entered into MATLAB in either of the following ways:
By entering each entry of the matrix individually.
u(1)=1;
u(2)=4;
u(3)=9;
Note that u(1) corresponds to the first entry of u, etc.
By typing the entries inside square brackets separated by spaces:
u=[1 4 9];
The transpose of u may be printed by typing u'.
Suppose the vector $v$ is given by: $$v=\begin{pmatrix}4\\5\\6\end{pmatrix}$$
This may be entered by typing:
v = [4;5;6];
Inside the square brackets the semicolon denotes a new row.
Vectors are sometimes referred to as arrays. This may be confusing so always look at the dimensions of the array to check the type.
The length of a vector v can be found by using the command length(v), which here gives:
>> length(v)
ans =
3
The size of a vector v can be found by using the command size(v), which here gives:
>> size(v)
ans =
3 1
This tells us that v has 3 rows and 1 column, and thus allows us to distinguish it from u, which has 1 row and 3 columns.
Now look up the commands length and size in the help files:
help length
help size
Matrices in MATLAB are $m\times n$ arrays of numbers.
Suppose the matrix $A$ is given by: $$A=\begin{pmatrix}1&2\\3&4\end{pmatrix}$$
This may be entered into MATLAB in either of the following ways:
By entering each entry of the matrix individually
A(1,1)=1;
A(1,2)=2;
A(2,1)=3;
A(2,2)=4;
The entry $A(i,j)$ corresponds to the entry in row $i$ and column $j$ of the matrix $A$.
By typing
A=[1 2; 3 4];
Use of ; inside the square brackets denotes a new row in the matrix.
The dimensions of a matrix A can be found by using the command size(A), which here gives
>> size(A)
ans =
2 2
Running the command length(A) on a matrix A yields the result 2, which is the bigger dimension of the matrix, so if A were a $4\times 6$ or a $6\times 4$ matrix, length(A) would yield the answer 6.
Editing vectors and matrices can be done by specifying the individual element.
For example, to change the value of 2 in the matrix A, above, to 5 we can type
A(1,2)=5;
An alternative method is to double-click on A in the Workspace window.
This opens a window containing the contents of the matrix A.
Click on the entry in the first row, second column, and change it to 5.
Sometimes we may wish to access only certain parts of a matrix or vector. There are a number of inbuilt MATLAB commands to help with this.
The matrix $$C=\begin{pmatrix}1&2&3&4\\5&6&7&8\\9&10&11&12\end{pmatrix}$$
may be entered in MATLAB as
C=[1 2 3 4; 5 6 7 8; 9 10 11 12];
To view the whole matrix we would type
C
To view the second column we would type
C(:,2)
To view the third row we would type
C(3,:)
To view the first two rows we would type
C(1:2,:)
To view the elements in both the last two rows and the last three columns we would type
C(2:3,2:4)
The following: C(2:end,2:end) would yield the same result.