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

2010/11/16 by Hieu, Doan The, Tuan, Huynh Dinh
#15A04 #FOS: Mathematics #Operator Algebras (math.OA) #Primary 15A86 #Secondary 15A18

paper · doi:10.48550/arxiv.1011.3739

Abstract

We study on what conditions on B_k, a linear transformation of rank r T(A)=∑_k=1^r\tr(AB_k)U_k where U_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.

Related

• Linear transformations on symmetric matrices
• Positive definite preserving linear transformations on symmetric matrix spaces
• Linear mappings on second symmetric product spaces that Preserve rank less than or equal to one
• Linear preservers of copositive and completely positive matrices
• Linear k-power preservers and trace of power-product preservers