Understand Matrix Norm: A Beginner Introduction – Deep Learning Tutorial

Matrix norm is one of important algorithm in deep learning. In this tutorial, we will introduce some basic features of matrix norm then tell you how to calculate it.

What is matrix norm?

A matrix norm of a matrix ||A|| is mapped from R^n*n to R, it is similar to vector norm and also has three features.

From above, we can find the matrix norm is a scalar, not a vector.

How to calculate l₁, l₂ and l_∞ matrix norm?

The  l₁, l₂ and l_∞ norm of a matrix A is defined as:

where δ_i is are the square root of eigenvalues of A^TA, δ_max is the largest in absolute value among δ_i.

Here is an example

The meaning of matrix norm

Matrix norm can be viewed as:

We can calculate matrix norm using tensorflow, here is an tutorial:

TensorFlow Calculate Matrix L1, L2 and L Infinity Norm: A Beginner Guide – TensorFlow Tutorial