l0-Norm, l1-Norm, l2-Norm, … , l-infinity Norm

Helpful for beginners

Rorasa's blog

I’m working on things related to norm a lot lately and it is time to talk about it. In this post we are going to discuss about a whole family of norm.

What is a norm?

Mathematically a norm is a total size or length of all vectors in a vector space  or matrices. For simplicity, we can say that the higher the norm is, the bigger the (value in) matrix or vector is. Norm may come in many forms and many names, including these popular name: Euclidean distance, Mean-squared Error, etc.

Most of the time you will see the norm appears in a equation like this:

$latex \left \| x \right \|$ where $latex x $ can be a vector or a matrix.

For example, a Euclidean norm of a vector $latex

a = \begin{bmatrix}
3
\\
-2
\\
1
\end{bmatrix}$ is $latex \left \| a \right…

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