Is this absolute value notation or something else?

Question

In this document, in Figure 1 (second to last page) there are several uses of $\| \;\;\|$:

Is this another notation for absolute value, or is this a notation for something to do with vectors/matrices?

Answer 1

As the document says immediately following the introduction:

This Wikipedia page has the definition of the $2$-norm and the $\infty$-norm of a vector. The definition is as follows: for a vector $x=(x_1,\ldots,x_m)\in\mathbb{R}^m$, the $p$-norm of $x$ is $$\|x\|_p:=(x_1^p+\cdots+x_m^p)^{1/p}$$ if $p$ is finite, and if $p=\infty$, we define $$\|x\|_\infty:=\max\{x_1,\ldots,x_m\}.$$