# How to Calculate the Norm of a Matrix in R (5 Examples) | norm() Function

In this R programming tutorial youâ€™ll learn how to **compute the norm of a matrix using the norm() function**.

The content of the tutorial looks like this:

Letâ€™s dig in:

## Creation of Example Data

Weâ€™ll use the following data as basement for this R tutorial:

set.seed(3826733) # Create example matrix my_mat <- matrix(sample(1:10, replace = TRUE, 20), ncol = 4) my_mat # Print example matrix |

set.seed(3826733) # Create example matrix my_mat <- matrix(sample(1:10, replace = TRUE, 20), ncol = 4) my_mat # Print example matrix

Have a look at the previous table. It shows that our example data contains five rows and four integer columns.

Letâ€™s compute different types of the norm of this matrix.

## Example 1: Compute One Norm of Matrix

Example 1 explains how to calculate the one norm of a matrix, i.e. the default specification of the norm function.

Have a look at the following R code:

norm(my_mat) # One norm # [1] 35 |

norm(my_mat) # One norm # [1] 35

The RStudio console has returned the one norm of our example matrix, i.e. 35.

## Example 2: Compute Infinity Norm of Matrix

The norm function provides different types of matrix norms.

Example 2 shows how to get the infinity norm of a matrix:

norm(my_mat, type = "I") # Infinity norm # [1] 28 |

norm(my_mat, type = "I") # Infinity norm # [1] 28

## Example 3: Compute Forbenius Norm of Matrix

This example illustrates how to return the Forbenius norm of a matrix:

norm(my_mat, type = "F") # Forbenius norm # [1] 29.20616 |

norm(my_mat, type = "F") # Forbenius norm # [1] 29.20616

## Example 4: Compute Maximum Modulus Norm of Matrix

This example explains how to compute the maximum modulus norm of a matrix:

norm(my_mat, type = "M") # Maximum modulus # [1] 10 |

norm(my_mat, type = "M") # Maximum modulus # [1] 10

## Example 5: Compute Spectral Norm / 2-Norm of Matrix

This example demonstrates how to calculate the spectral norm (or 2-norm) of a data matrix.

norm(my_mat, type = "2") # Spectral / 2-norm # [1] 26.84743 |

norm(my_mat, type = "2") # Spectral / 2-norm # [1] 26.84743

## Video & Further Resources

Do you need further information on the R programming codes of this tutorial? Then you may have a look at the following video on my YouTube channel. Iâ€™m explaining the content of this tutorial in the video.

*The YouTube video will be added soon.*

In addition, you may have a look at the other posts on this homepage. I have published several articles already:

- Multiply Rows of Matrix by Vector
- Calculate Determinant of Matrix in R
- Matrix Cross Product in R
- QR Matrix Decomposition in R
- Inverse of Matrix in R
- All R Programming Tutorials

Summary: In this post you have learned how to **apply the norm() function** in R. Please let me know in the comments section below, if you have any further questions.

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