  We give a short proof of a recent result of Drury on the positivity of a
$3\times 3$ matrix of the form $(\|R_i^*R_j\|_{\rm tr})_{1 \le i, j \le 3}$ for
any rectangular complex (or real) matrices $R_1, R_2, R_3$ so that the
multiplication $R_i^*R_j$ is compatible for all $i, j$, where $\|\cdot\|_{\rm
tr}$ denotes the trace norm. We then give a complete analysis of the problem
when the trace norm is replaced by other unitarily invariant norms.
