We consider the projected semi-definite and Euclidean distance cones onto a subset of the matrix entries. These two sets are precisely the input data defining feasible semi-definite and Euclidean distance completion problems. We characterize when these sets are closed, and use the boundary structure of these two sets to elucidate the Krislock-Wolkowicz facial reduction algorithm. In particular, we show that under a chordality assumption, the ``minimal cones'' of these problems admit combinatorial characterizations.

## Article

View Coordinate shadows of semi-definite and Euclidean distance matrices