  Finite dimensional linear spaces (both complex and real) with indefinite
scalar product [.,.] are considered. Upper and lower bounds are given for the
size of an indecomposable matrix that is normal with respect to this scalar
product in terms of specific functions of v = min{v-, v+}, where v-, (v+) is
the number of negative (positive) squares of the form [x,x]. All the bounds
except for one are proved to be strict.
