  We provide an effective single-matrix criterion, in terms of what we call the
elementary Pick matrix, for the solvability of the noncommutative
Nevanlinna-Pick interpolation problem in the row ball, and provide some
applications. In particular we show that the so-called "column-row property"
fails for the free semigroup algebras, in stark contrast to the analogous
commutative case. Additional applications of the elementary Pick matrix include
a local dilation theorem for matrix row contractions and interpolating
sequences in the noncommutative setting. Finally we present some numerical
results related to the failure of the column-row property.

Functional Analysis