Let
be a field, and
let
be a matrix
with entries in
,
where
is a placeholder symbol for nonspecified entries. The
minimum rank
is the smallest value of the ranks of all matrices obtained from
by replacing the
symbols with arbitrary
elements in
. A
triangularrelaxation is obtained
by placing
at several
specified entries of
so that
does not appear as a submatrix of
with any
in
. We show that
can be arbitrarily
large even if
for any
triangular relaxation
of
.
This answers a question asked by Johnson and Whitney in 1991.