Ottawa, 7 - 11 juin 2021
We present two conditions equivalent to $C$ failing to admit a doubleton projection: a property related to (but stronger than) connectedness called $B^\circ$-Connectedness, and a property we call Locally-Determined Set Curvature.
These results tell us some non-trivial geometric facts about Chebyshev sets in real Hilbert Spaces. Such sets are the subject of a long-standing open problem known as the Chebyshev Conjecture.
In this paper, we provide a formula for the more general problem of finding the projection onto the set of rectangular matrices with prescribed scaled row and column sums. Our approach is based on computing the Moore-Penrose inverse of a certain linear operator associated with the problem. In fact, our analysis holds even for Hilbert-Schmidt operators and we do not have to assume consistency. We also perform numerical experiments featuring the new projection operator.