The strong Arnold property for a real symmetric matrix 
indexed by the vertices of a simple
graph 
means that the only real symmetric
matrix 
satisfying 
,
for all vertices 
, and 
whenever 
and 
are adjacent is 
. An invertible
matrix automatically has the strong Arnold property.
The condition is part of the definition of the Colin de Verdière invariant, which maximizes nullity over a restricted class of symmetric matrices.
