Question
Answer and Explanation
Creating an identity matrix in R is straightforward using the diag() function. An identity matrix is a square matrix with ones on the main diagonal and zeros elsewhere. Here's how you can create one:
1. Using the diag() function:
- The diag() function can create a diagonal matrix. If you pass a single positive integer n to it, it creates an n x n identity matrix.
2. Example Code:
# Create a 5x5 identity matrix
identity_matrix <- diag(5)
# Print the identity matrix
print(identity_matrix)
- This code will create a 5x5 identity matrix. The output will be:
[,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
3. Explanation:
- The diag(5) command tells R to construct a diagonal matrix with dimension 5x5, where the diagonal elements are all set to 1, effectively creating the identity matrix. This is a fundamental operation in linear algebra and often used as a starting point for more complex matrix manipulations.
4. Applications:
- Identity matrices are crucial in many linear algebra operations, such as verifying matrix inverses or serving as neutral elements in matrix multiplication.
By using the diag() function, you can easily create identity matrices of any size in R, facilitating various mathematical and statistical computations. Remember to choose the appropriate size based on your specific application.