What notation is used to represent the normalised or z-score value of a vector $x$?
Or, given:
$? = \dfrac {x - \mu } {\sqrt{\sigma^2}}$
Where $\mu$ and $\sigma$ are calculated across the whole population of $x$.
Is there a canonical, agreed or widely used symbol to replace "$?$"?
My specific context is batch normalisation. If the vector $z = Wa + b$ is the biased, weighted sum of a layer in a neural network, what notation would I use to represent that vector after it has been normalised?
It may be a little confusing since $z$ is a commonly used variable for this pre-activation weighted sum, and I want the notation to represent the z-score version of $z$.)
Is the answer the same in the context of scalars, vectors and matrices?
A similar question exists for physics, but I would like to know the answer from the machine learning perspective.