ELA, Volume 16, pp. 248-283, September 2007, abstract.

Comparison of Congruences and Strict Equivalences for Real, 
Complex, and Quaternionic Matrix Pencils with Symmetries

Leiba Rodman

The equivalence relations of strict equivalence and congruence 
of real and complex  matrix pencils with symmetries are compared, 
depending on whether the congruence matrices are real, complex, 
or quaternionic. The obtained results are applied to comparison 
of congruences of matrices, over the reals, the complexes, and 
the quaternions.