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 <- matrix(0, 5, 5) diag(mat) <- 1

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 <- diag(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

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 <- diag(nrow=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 <- matrix(0, 5, 5) #make diagonal values 1 diag(ident) <- 1 #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