I have an algorithms class and a question is referring to $||X||$. I know that $|X|$ would be referring to the size of an object, I have searched around and only found information about vectors that I do not entirely understand.
What does this double bar symbol mean? Apparently the symbols are interchangeable, is this true?
In the simplest case, for a vector $x\in\mathbb{R}^n$ such that $x:=(x_1,x_2,\dots,x_n)$, we can define $$ ||x||:=\sqrt{\sum_{i=1}^n x_i^2} $$
Now, if $n=1$ (that is, if $x$ is a real number) we have $$ ||x||=\sqrt{x^2}=|x| $$