I am facing problem in understanding math symbol? I am trying to understand a symbol and facing difficulties to solve it!!
$$\|F\|^2$$
where $F$ is vector (suppose $F = [1 \; 2 \; 3]$). How to solve this ? I know following symbol only
$$\|F\| = \left( (1)^2 + (2)^2 + (3)^2 \right)^{1/2}$$
Kindly help me out as I have never seen the said symbol before.
Also can some one tell me the difference between $\|F\|^2$ and $\|F\|_2$?
 A: $\|F\|^2$ ultimately would mean the same thing as $\|F\|$, just now squared - so it's simpler than you think. If $\|F\|$ denotes the Euclidean norm as mentioned in your post for the vector $F = [ 1 \; 2 \; 3 ]$, then
$$\|F\| = \sqrt{1^2 + 2^2 + 3^2}$$
and thus
$$\|F\|^2 = \left(\sqrt{1^2 + 2^2 + 3^2}\right)^2 = 1^2 + 2^2 + 3^2$$
Of course, $\|F\|$ might mean a different norm than this Euclidean norm, but usually it is well-understood what norm is meant whenever the symbol is used. The Euclidean norm is often given the shorthand $\|F\|_2$ to help make it more clear which norm we're referring to. 
Similar related norms exist, anecdotally. For example, let $p$ be a real number greater than or equal to $1$, and let $F$ denote the vector $[ x_1 \; \cdots \; x_n ]$. Then we can define the $p$ norm $\|\cdot \|_p$ by
$$\|F\|_p = \left( \sum_{i=1}^n x_i^p \right)^{1/p}$$
with the Euclidean norm having the special case of $p=2$. If you haven't been introduced to other types of norms yet, though, don't worry so much about all this "different kinds of norms" stuff, it'll become clearer in due time.
