Isoconjunctivity of hermitian matrices Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/vt150p05t

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  • In this thesis we define two nxn matrices T and S to be isoconjunctive if there exists an nxn nonsingular hermitian matrix H such that T = HSH. We then proceed to establish necessary and sufficient conditions that two nxn matrices T and S be isoconjunctive in the case where both T and S are hermitian. The results are obtained by decomposing the problem into two cases. In Chapter II we consider the case where TS is nonsingular. In Chapter III we first obtain a canonical form, under contragradient conjunctivity, for a pair of nxn hermitian matrices whose product is nilpotent. This result is used to obtain the conditions in the nilpotent case. In Chapter IV we draw together the results of Chapter II and Chapter III. Also in Chapter IV we give necessary and sufficient conditions on a pair of nxn hermitian matrices T and S that there exist a positive definite matrix H such that T = HSH.
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