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 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
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 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
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 5x2 matrix. We concatenate a third column and verify the dimension is 5x3
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 4x6 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 6x3
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_b, add_row) # Check the dimension dim(matrix_c)
Output:
## [1] 6 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
