In linear algebra, the identity matrix is a square matrix with ones on the main diagonal and zeros everywhere else.
You can create the identity matrix in R by using one of the following three methods:
#create identity matrix using diag()
diag(5)
#create identity matrix using diag() with explicit nrow argument
diag(nrow=5)
#create identity matrix by creating matrix of zeros, then filling diagonal with ones
mat
Each of these methods lead to the same result.
The following examples show how to use each of these methods in practice.
Example 1: Create Identity Matrix Using diag()
The following code shows how to use the diag() function to create an identity matrix with 5 rows and 5 columns:
#create 5x5 identity matrix
ident
#view matrix
ident
[,1] [,2] [,3] [,4] [,5]
[1,] 1 0 0 0 0
[2,] 0 1 0 0 0
[3,] 0 0 1 0 0
[4,] 0 0 0 1 0
[5,] 0 0 0 0 1
The result is a 5×5 square matrix with ones on the main diagonal and zeros everywhere else.
Example 2: Create Identity Matrix Using diag(nrow)
The following code shows how to use the diag(nrow) function to create a 5×5 identity matrix:
#create 5x5 identity matrix ident 5) #view matrix ident [,1] [,2] [,3] [,4] [,5] [1,] 1 0 0 0 0 [2,] 0 1 0 0 0 [3,] 0 0 1 0 0 [4,] 0 0 0 1 0 [5,] 0 0 0 0 1
Example 3: Create Identity Matrix in Two Steps
The following code shows how create a 5×5 identity matrix by first creating a 5×5 matrix with all zeros, then converting the main diagonal values to be ones:
#create 5x5 matrix with zeros in all positions
ident #make diagonal values 1
diag(ident) #view matrix
ident
[,1] [,2] [,3] [,4] [,5]
[1,] 1 0 0 0 0
[2,] 0 1 0 0 0
[3,] 0 0 1 0 0
[4,] 0 0 0 1 0
[5,] 0 0 0 0 1
Notice that each of the three methods produce the exact same identity matrix.
Additional Resources
The following articles provide helpful introductions to the identity matrix:
Khan Academy: Introduction to the Identity Matrix
Wikipedia: A Comprehensive Explanation of the Identity Matrix
The following articles explain how to perform other common matrix operations in R:
How to Perform Matrix Multiplication in R
How to Perform Element-Wise Multiplication in R
How to Plot the Rows of a Matrix in R