Comparison of congruences and strict equivalences for real, complex, and quaternionic matrix pencils with symmetries

Abstract

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.