What is a Matrix?

A matrix is a 2-dimensional array that has m number of rows and n number of columns. In other words, matrix is a combination of two or more vectors with the same data type.

Note: It is possible to create more than two dimensions arrays with R.

How to Create a Matrix in R

We can create a matrix with the functionmatrix(). This function takes three arguments:

matrix(data, nrow, ncol, byrow = FALSE)

Arguments:

  • data: The collection of elements that R will arrange into the rows and columns of the matrix
  • nrow: Number of rows
  • ncol: Number of columns
  • byrow: The rows are filled from the left to the right. We use byrow = FALSE (default values), if we want the matrix to be filled by the columns i.e. the values are filled top to bottom.

Let’s construct two 5x2 matrix with a sequence of number from 1 to 10, one with byrow = TRUE and one with byrow = FALSE to see the difference.

# Construct a matrix with 5 rows that contain the numbers 1 up to 10 and byrow =  TRUE 
matrix_a <- matrix(1:10, byrow = TRUE, nrow = 5)
matrix_a
##      [,1] [,2]
## [1,]    1    2
## [2,]    3    4
## [3,]    5    6
## [4,]    7    8
## [5,]    9   10
# Print dimension of the matrix with dim()
dim(matrix_a)
## [1] 5 2
# Construct a matrix with 5 rows that contain the numbers 1 up to 10 and byrow = FALSE
matrix_b <-matrix(1:10, byrow = FALSE, nrow = 5)
matrix_b
##      [,1] [,2]
## [1,]    1    6
## [2,]    2    7
## [3,]    3    8
## [4,]    4    9
## [5,]    5   10
# Print dimension of the matrix with dim()
dim(matrix_b)
## [1] 5 2

Note: Using command matrix_b <-matrix(1:10, byrow = FALSE, ncol = 2) will have same effect as above.

You can also create a 4x3 matrix using ncol. R will create 3 columns and fill the row from top to bottom. Check an example

matrix_c <-matrix(1:12, byrow = FALSE, ncol = 3)
matrix_c
##      [,1] [,2] [,3]
## [1,]    1    5    9
## [2,]    2    6   10
## [3,]    3    7   11
## [4,]    4    8   12

Example:

dim(matrix_c)
## [1] 4 3

Add a Column to a Matrix with the cbind()

You can add a column to a matrix with the cbind() command. cbind() means column binding. cbind() can concatenate as many matrix or columns as specified. For example, our previous example created a 5x2 matrix. We concatenate a third column and verify the dimension is 5x3

Example 1:

# concatenate c(1:5) to the matrix_a
matrix_a1 <- cbind(matrix_a, c(1:5))
# Check the dimension
dim(matrix_a1)
## [1] 5 3

Example 2:

matrix_a1
##      [,1] [,2] [,3]
## [1,]    1    2    1
## [2,]    3    4    2
## [3,]    5    6    3
## [4,]    7    8    4
## [5,]    9   10    5

Example 3:

We can also add more than one column. Let’s see the next sequence of number to the matrix_a2 matrix. The dimension of the new matrix will be 4x6 with number from 1 to 24.

matrix_a2 <- matrix(13:24, byrow = FALSE, ncol = 3)

Example 4:

matrix_c <- matrix(1:12, byrow = FALSE, ncol = 3)       
matrix_d <- cbind(matrix_a2, matrix_c)
dim(matrix_d)
## [1] 4 6

NOTE: The number of rows of matrices should be equal for cbind work

cbind() concatenate columns, rbind() appends rows. Let’s add one row to our matrix_c matrix and verify the dimension is 5x3

matrix_c <- matrix(1:12, byrow = FALSE, ncol = 3)
# Create a vector of 3 columns
add_row <- c(1:3)
# Append to the matrix
matrix_c <- rbind(matrix_c, add_row)
# Check the dimension
dim(matrix_c)
## [1] 5 3

Slice a Matrix

We can select elements one or many elements from a matrix by using the square brackets []. This is where slicing comes into the picture.

For example:

  • matrix_c[1, 2] selects the element at the first row and second column.
  • matrix_c[1:3, 2:3] results in a matrix with the data on the rows 1, 2, 3 and columns 2, 3.
  • matrix_c[, 1] selects all elements of the first column.
  • matrix_c[1, ] selects all elements of the first row.

Here is the output you get for the above codes

 

A work by Gianluca Sottile

gianluca.sottile@unipa.it