New answers tagged packing-and-covering
5
votes
How many non-orthogonal vectors fit into a complex vector space?
Jan Nienhaus's answer treats the case $\epsilon<\frac{1}{D}$. Here's a generalization that works whenever $\epsilon<\frac{1}{\sqrt{D}}$:
$$ N \leq \frac{1-\epsilon^2}{1 - D\epsilon^2}\cdot D. $$
...
- 7,525
6
votes
How many non-orthogonal vectors fit into a complex vector space?
While volume comparison will give you a rough estimate for any value of $\varepsilon$, the sharp estimate is that, for small enough $\varepsilon$, $N\le D$.
One way to get this is by showing that your ...
- 521
4
votes
How many non-orthogonal vectors fit into a complex vector space?
This is a packing problem in the complex projective space $CP^{D-1}$ of dimension $D-1$ with its Fubini-Study metric. Since the volume of $CP^{D-1}$ is known, you can use the same argument by ...
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