Matrices in R language
This article is about matrices in R language.
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