Matrix is a set of elements, sorted in rows and columns. Matrix of 2×3 size is a matrix with 2 rows and 3 columns.

## Example 1 – create matrix

You can use a matrix function to create matrix. The first argument is a number of items in matrix. In following arguments we have to declare the size of matrix – either by defining number of rows (nrow argument) or by defining of number of columns (ncol argument).

Lets create the matrix myMatrix with numbers from 1 to 20, sorted in 4 fows (or 5 columns). The sequence from 1 to 20 can be created by seq(1,20).

The command is:

`> myMatrix = matrix(seq(1,20), nrow = 4)`

or:

`> myMatrix = matrix(seq(1,20), ncol = 5)`

The results for both ways are identical.

```> myMatrix
[,1] [,2] [,3] [,4] [,5]
[1,]    1    5    9   13   17
[2,]    2    6   10   14   18
[3,]    3    7   11   15   19
[4,]    4    8   12   16   20
```

The numbers are inserted by columns. To insert them by rows, use the byrow voluntary argument:

byrow = TRUE.

## Example 2 – matrix operations

With matrices, of course, we can perform all routine operations in R. If we add a number to the matrix or multiply it by a number, then this operation is applied to each element of the matrix individually. For example:

```> myMatrix * 2
[,1] [,2] [,3] [,4] [,5]
[1,]    2   10   18   26   34
[2,]    4   12   20   28   36
[3,]    6   14   22   30   38
[4,]    8   16   24   32   40```

If we used myMatix * myMatix, then R would multiply the first element of myMatrix with the first, second with the other, etc. To perform a “real” multiplication of matrices, the operator should be bound by percentages. For example, to multiply myMatrix by a matrix transposed to myMatrix, just write:

```> myMatrix %*% t(myMatrix)
[,1] [,2] [,3] [,4]
[1,]  565  610  655  700
[2,]  610  660  710  760
[3,]  655  710  765  820
[4,]  700  760  820  880```

We see that transposition is performed by the function t. (Transposition of a matrix means switching of rows and columns (the first row of the matrix is the first column of the matrix to which it is transposed, etc.).)

## Example 3 – select item from matrix

We can select a row, column, or element from a matrix. To select the item from third row and second column use this command:

```> myMatrix[3,2]
[1] 7```

Therefore, the index of an element is entered into square brackets, so that the first index is the row number and the second index is a column number.

To get the entire third line, just leave a blank space instead of the column index:

```> myMatrix[3, ]
[1]  3  7 11 15 19
```

Analogously – to get the second row, leave the row index empty.

```> myMatrix[ ,2]
[1] 5 6 7 8
```

Any item in matrix can be changed by defining a specific value. For example the item in third row and second column can be chaned to 1000 by this command:

```< myMatrix[3,2] = 1000
< myMatrix
[,1] [,2] [,3] [,4] [,5]
[1,]    1    5    9   13   17
[2,]    2    6   10   14   18
[3,]    3 1000   11   15   19
[4,]    4    8   12   16   20```