Completing a Matrix so as to Minimize the Rank

Abstract

The problem of choosing the missing entry in the partial matrix $\begin{bmatrix}\text{A} & \text{C} \\\text{B} & ? \end{bmatrix}$ so as to minimize the rank, which had earlier been solved only under a somewhat restrictive hypothesis, is here given a general solution, with description of the full solution set.

The author thanks NSERC of Canada for financial support, and the Indian Statistical Institute Delhi Centre, where this work was begun.