Linear Algebra – What Does Double Absolute Value Notation Mean?

Question

Here,

$$\left\lVert\frac{\partial\bf x}{\partial s}\times\frac{\partial\bf x}{\partial t}\right\rVert$$

the inside will at last be a vector. and two absolute value signs have covered it. what does it mean?

Can someone explain it to me? $||\vec a||$

Answer 1

$\| a \|$ in general means the "norm" of $a$. Most commonly it means the Euclidean norm of the vector $a$. You could say "the geometric length of $a$" or "the magnitude of $a$" to refer to the same concept.

Be careful: there are many other norms that can be used to measure vectors, as well as norms that can be used to measure different sorts of objects entirely.