Understand Matrix Norm: A Beginner Introduction – Deep Learning Tutorial

By | July 6, 2020

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 Rn*n to R, it is similar to vector norm and also has three features.

matrix norm properties

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:

matrix l1 l2 and l infinity norm

where δi is are the square root of eigenvalues of ATAδmax is the largest in absolute value among δi.

Here is an example

an example for calculating the norm of matrix A

The meaning of matrix norm

Matrix norm can be viewed as:

The meaning of matrix norm

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

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