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.
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 δi is are the square root of eigenvalues of ATA, δmax is the largest in absolute value among δi.
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: