  The aim of this paper is to study symmetries of linearly singular
differential equations, namely, equations that can not be written in normal
form because the derivatives are multiplied by a singular linear operator.
  The concept of geometric symmetry of a linearly singular differential
equation is introduced as a transformation that preserves the geometric data
that define the problem. It is proved that such symmetries are essentially
equivalent to dynamic symmetries, that is, transformations mapping solutions
into solutions. Similar results are given for infinitesimal symmetries.
  To study the invariance of several objects under the flows of vector fields,
a careful study of infinitesimal variations is performed, with a special
emphasis on infinitesimal vector bundle automorphisms.
