On positive definite preserving linear transformations of rank r on real symmetric matrices
Abstract
We study on what conditions on Bk, \ a linear transformation of rank r form T(A)=Σk=1r(ABk)Uk where Uk,\ k=1,2,..., r are linear independent and all positive definite; is positive definite preserving. We give some first results for this question. For the case of rank one and two, the necessary and sufficient conditions are given. We also give some sufficient conditions for the case of rank r.
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