# How to Use the diag() Function in R

The diagonal of a matrix refers to the elements along the diagonal entries of the matrix.

Since matrices are used in nearly all statistical algorithms and formulas, you may often have a need to either extract or replace the elements along the diagonal of a matrix.

The easiest way to do so is by using the diag() function from base R, which is designed for this exact task.

The diag() function uses the following basic syntax:

diag(x = 1, nrow, ncol, names = TRUE)

where:

• x: Name of the matrix
• nrow, ncol: Optional dimensions for the result when x is not a matrix
• names: TRUE or FALSE to indicate if resulting matrix should inherit names from the dimensions of the original matrix

There are two common ways to use the diag() function in practice in R:

Method 1: Use diag() to Retrieve Elements from Diagonal of Matrix

```#extract diagonal elements from matrix named my_matrix
diag(my_matrix)
```

This particular example uses the diag() function to simply extract the diagonal elements from the matrix named my_matrix.

Method 2: Use diag() to Set Elements on Diagonal of Matrix

```#set diagonal elements of matrix named my_matrix to zero
diag(my_matrix) <- 0```

This particular example uses the diag() function to set the values of each of the diagonal elements of the matrix named my_matrix to be zero.

The following examples show how to use each of these methods in practice.

Note: The diag() function is typically used when working with square matrices (matrices that have the same number of columns and rows) but it will still return the diagonal elements of a non-square matrix without causing any errors in your code.

## Example 1: Use diag() to Retrieve Elements from Diagonal of Matrix

Suppose we create the following matrix named my_matrix that contains 3 rows and 3 columns:

```#create 3x3 matrix
my_matrix <- matrix(c(2, 5, -3, 0, 2, 6, 5, 5, 8), nrow=3)

#view matrix
my_matrix

[,1] [,2] [,3]
[1,]    2    0    5
[2,]    5    2    5
[3,]   -3    6    8
```

Suppose that we would like to extract only the elements along the diagonal of the matrix.

We can use the diag() function with the following syntax to do so:

```#extract values along the diagonal of the matrix
diag(my_matrix)

[1] 2 2 8
```

This returns the values 2, 2 and 8, which represent the three values along the diagonal of the matrix.

## Example 2: Use diag() to Set Elements on Diagonal of Matrix

Suppose we create the following matrix named my_matrix that contains 3 rows and 3 columns:

```#create 3x3 matrix
my_matrix <- matrix(c(2, 5, -3, 0, 2, 6, 5, 5, 8), nrow=3)

#view matrix
my_matrix

[,1] [,2] [,3]
[1,]    2    0    5
[2,]    5    2    5
[3,]   -3    6    8
```

Suppose that we would like to set the values of the elements along the diagonal of the matrix to all be equal to zero.

We can use the diag() function with the following syntax to do so:

```#set all elements along diagonal of matrix to be zero
diag(my_matrix) <- 0

#view updated matrix
my_matrix

[,1] [,2] [,3]
[1,]    0    0    5
[2,]    5    0    5
[3,]   -3    6    0
```

Notice that each of the values along the diagonal of the matrix are now equal to zero, just as we specified.