Indefinite product of matrices in the context of indefinite inner product spaces

Abstract

The primary motivation of this thesis is to develop a theory of indenite inner newlineproduct spaces based on an indenite matrix multiplication This is necessitated newlineby the fact that the usual matrix multiplication is not well dened in an indenite newlineinner product space The distinct advantages of the proposed approach are newlinei The defect mentioned above is rectied and hence the new indenite matrix newlineproduct is more appropriate in the setting of the indenite inner product newlinespacesii The approach enables us to develop a theory parallel to the Euclidean case newlineand also view the Euclidean space as a particular case of indenite inner newlineproduct spaceThe thesis comprises of ve chapters newline newline