What do you mean by ||x|| in hyper plane?
I am reading my linear algebra notes, I don't understand ||x|| meaning?
1 Answer
$\begingroup$$\Vert x\Vert$ is the norm of $x$. Intuitively it's the "length of the vector", or the "distance of the point from the origin".
In your case, you're implicitly working with $\Vert x\Vert = \sqrt{x_1^2+x_2^2+\cdots+ x_n^2}$. You'll see that this is pythagoras' theorem to get the length of a diagonal in a right angled triangle in $n$-dimensions. There are other ways you can define $\Vert x\Vert$, but the one defined above enables you to have a notion of angles in $\mathbb{R}^n$, so it's the standard unless otherwise stated.
If you think of it as the distance of the point from the origin, it's clear that "$\Vert x \Vert ≤ r$ for all $x\in T$" is a sensible definition for boundedness, because it's saying "no points in $T$ are more than $r$ away from the origin".
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