English

On positive definite preserving linear transformations of rank $r$ on real symmetric matrices

Operator Algebras 2010-11-23 v2

Abstract

We study on what conditions on Bk,B_k, \ a linear transformation of rank rr \label{form} T(A)=\sum_{k=1}^r\tr(AB_k)U_k where Uk, k=1,2,...,rU_k,\ 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.r.

Keywords

Cite

@article{arxiv.1011.3739,
  title  = {On positive definite preserving linear transformations of rank $r$ on real symmetric matrices},
  author = {Doan The Hieu and Huynh Dinh Tuan},
  journal= {arXiv preprint arXiv:1011.3739},
  year   = {2010}
}

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5 pages