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Unfamiliar Norm Notation

OhMyMarkov

Member
Mar 5, 2012
83
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
Feb 5, 2012
1,621
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
Mar 5, 2012
83
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.