All Questions
2
questions
0
votes
1
answer
21
views
$L_1$ distance between re-normalized points
Let $\mathbf{x},\mathbf{y} \in (0, \infty)^d$. Are there general relations between
$
\Vert \mathbf{x}-\mathbf{y} \Vert_1
$
and
$
\left\Vert
\frac{\mathbf{x}}{\Vert \mathbf{x}\Vert_1}
-\frac{\mathbf{y}...
- 1,786
1
vote
1
answer
298
views
Bounding the dot product of two planar unit vectors.
Does there exist a continuous, monotone increasing function $f\colon[0,2]\to [0,1]$, satisfying $f(0)=0$ and $f(1)=1$, such that for all vectors $(a_1,b_1),(a_2,b_2)\in \mathbb{R}^2$ of unit length, i....
- 2,684