Understand Frobenius Norm: A Beginner Guide – Deep Learning Tutorial

By | May 18, 2020

Frobenius Norm is somtimes called the Hilbert-Schmidt norm, in this tutorial, we will introduce some basic knowlege for deep learning beginners.

The formula of Frobenius Norm

Frobenius Norm is defined as:

Frobenius Norm formula

where A is a m*n matrix. I can find the value of frobenius norm is a scalar.

How to calculate the value of frobenius norm?

It is easy to compute frobenius norm in numpy, here is an example:

import numpy as np

A = np.array([[1, 2, 3],[4, 5, 6]])
F = np.linalg.norm(A)
print(F)

In this example, A is a 2*3 matrix, we can use numpy.linalg.norm() to calculate its frobenius norm value, the value is:

9.53939201417

Feature of Frobenius Norm

General properties of frobenius norm are:

the properties of matrix norms

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