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 function matrix(). 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 5×2 matrix with a sequence of number from 1 to 10, one with byrow = TRUE and one with byrow = FALSE to see the difference.

matrix_a <-matrix(1:10, byrow = TRUE, nrow = 5)
matrix_a

Output:

Print dimension of the matrix with dim()

# Print dimension of the matrix with dim()
dim(matrix_a)

Output:

## [1] 5 2

Construct a matrix with 5 rows that contain the numbers 1 up to 10 and byrow = FALSE

# 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

Output:

Print dimension of the matrix with dim()

# Print dimension of the matrix with dim()
dim(matrix_b)

Output:

## [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 4×3 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

Output:

##       [,1] [,2] [,3]
## [1,]    1    5    9
## [2,]    2    6   10
## [3,]    3    7   11
## [4,]    4    8   12

Example:

dim(matrix_c)

Output:

## [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 5×2 matrix. We concatenate a third column and verify the dimension is 5×3

Example:

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

Output:

## [1] 5 3

Example:

matrix_a1

Output

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

Example:

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 4×6 with number from 1 to 24.

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

Output:

##      [,1] [,2] [,3]
## [1,]   13   17   21
## [2,]   14   18   22
## [3,]   15   19   23
## [4,]   16   20   24

Example:

matrix_c <-matrix(1:12, byrow = FALSE, ncol = 3)		
matrix_d <- cbind(matrix_a2, matrix_c)
dim(matrix_d)

Output:

## [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 5×3

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)

Output:

## [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