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Results tagged with convex-geometry
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user 11236
A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...
3
votes
Accepted
Convex Hull of Outer Products of (Normalised) Nonnegative Vectors
Your characterization of $\text{conv} (\mathcal{A})$ needs one additional restriction---that $M$ is positive semidefinite (the equivalence of these two sets follows fairly quickly from the spectral de …
- 6,351
5
votes
1
answer
256
views
Dimension reduction for non-negativity of elementary symmetric polynomials
Fix integers $1 \leq k \leq n$ and suppose $\mathbf{x} \in \mathbb{R}^n$ is such that $e_j(x_1,x_2,\ldots,x_n) \geq 0$ for all $1 \leq j \leq k$, where $e_j$ is the $j$-th elementary symmetric polynom …
- 6,351
3
votes
Is the set of two-qubit absolutely separable states convex, and if so, what are its John ell...
There are two slightly different questions here (even without discussing John ellipsoids, which I do not know the answer to), so I'll try to be careful in my answer.
Question 1: Is the set of absolute …
- 6,351
12
votes
Conditions for including cones
Iosif Pinelis already gave a nice solution to show that the answer is "no" for sets of infinitely many vectors, and thus for $N$ very large. I'll show that the answer is also "no" even for some set of …
- 6,351