# Unfamiliar Norm Notation

#### OhMyMarkov

##### Member
Hello everyone!

I came accross, in a reading, an unfamiliar norm notation: $||A-B||_{2,a}$ where $a$ is the standard deviation of a Gaussian kernel. Now I know that the index 2 represents the $\ell _2$ norm, but what about the $a$?

Moreover, is the matrix norm defnied in a similar way to the vector norm?

Any help is apptreciated!

#### Sudharaka

##### Well-known member
MHB Math Helper
Hello everyone!

I came accross, in a reading, an unfamiliar norm notation: $||A-B||_{2,a}$ where $a$ is the standard deviation of a Gaussian kernel. Now I know that the index 2 represents the $\ell _2$ norm, but what about the $a$?

Moreover, is the matrix norm defnied in a similar way to the vector norm?

Any help is apptreciated!
Hi OhMyMarkov,

The definition of the matrix norm and the notation you are taking about are explained here.

Kind Regards,
Sudharaka.

#### OhMyMarkov

##### Member
Thank you, Sudharaka,

I may need to point this out in case someone else comes across it in the future: this notation means the Element-wise (or Frobenius I guess) norm of the 2D-convolution of A with a Gaussian kernel of standard deviation a.