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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 …
Nathaniel Johnston's user avatar
2 votes
Accepted

Known Results on Convexity of Numerical Range

The only result of this nature that I'm aware of (beyond the two cases involving $M$ and $N$ that you've listed) is Theorem 3.1 in "C.-K. Li and Y.-T. Poon. Convexity of the joint numerical range. SIA …
Nathaniel Johnston's user avatar