H-SELF-ADJOINT AND H-UNITARY MATRIX PENCILS

A square matrix pencil lambda A - B is said to be H-selfadjoint (H-uni tary) if it satisfies AHB = B*HA (A*HA = B*HB) for some invertible He rmitian H. Attention is focused on regular pencils (i.e., det (lambda A B) not equivalent to 0) for which A and B are both singular. Canonic al forms for the relation (A, B, H) similar to (Y-1 AX, Y-1 BX, YHY) are obtained in both the complex and real cases. Also, a characterizat ion is given for those real matrices A which are H-unitary for some H, i.e., A(T) HA = H for some invertible, real symmetric H.