On indecomposable normal matrices in spaces with indefinite scalar product Original Research Article

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.