  VBP is the class of polynomial families that can be computed by the
determinant of a symbolic matrix of the form $A_0 + \sum_{i=1}^n A_ix_i$ where
the size of each $A_i$ is polynomial in the number of variables (equivalently,
computable by polynomial-sized algebraic branching programs (ABP)). A major
open problem in geometric complexity theory (GCT) is to determine whether VBP
is closed under approximation. The power of approximation is well understood
for some restricted models of computation, e.g., the class of depth-two
circuits, read-once oblivious ABPs (ROABP), monotone ABPs, depth-three circuits
of bounded top fan-in, and width-two ABPs. The former three classes are known
to be closed under approximation [Bl"{a}ser, Ikenmeyer, Mahajan, Pandey, and
Saurabh (2020)], whereas the approximative closure of the last one captures the
whole class of polynomial families computable by polynomial-sized formulas
[Bringmann, Ikenmeyer, and Zuiddam (2017)].
  In this work, we consider the subclass of VBP computed by the determinant of
a symbolic matrix of the form $A_0 + \sum_{i=1}^n A_ix_i$ where for each $1\leq
i \leq n$, $A_i$ is of rank one. It has been studied extensively
[Edmonds(1968), Edmonds(1979)] and efficient identity testing algorithms are
known [Lov"{a}sz (1989), Gurjar and Thierauf (2020)]. We show that this class
is closed under approximation. In the language of algebraic geometry, we show
that the set obtained by taking coordinatewise products of pairs of points from
(the Pl\"{u}cker embedding of) a Grassmannian variety is closed.
