# What does this || symbol mean?

I am trying to understand this paper, but in this paper the following || symbol is frequently used.

$$p_i(j) \propto \exp \{ - \| A x_i - A x_j \|_2^2\}$$

I wonder to know what does it mean, what are these two 2 are doing here?

And also wonder to know does the above || symbol has different meaning than the below || symbol (considering there is only one 2 here)?

$$p_i(j) \propto \exp \left\{ -\dfrac{\|x_i - x_j\|^2}{2 \sigma_i^2} \right\}$$

• $||\cdot||$ is the norm. See en.wikipedia.org/wiki/Norm_%28mathematics%29 – Alex Silva Jan 15 '15 at 16:20
• what are those two 2? – dariush Jan 15 '15 at 16:23
• The lower $2$ probably means it's the 2-norm (the standard euclidean distance), and the upper is probably just an exponent. – Henrik Jan 15 '15 at 16:24