Details

Autor(en) / Beteiligte

• ter Horst, S.
• van der Merwe, A.

Titel

Hill representations for ∗-linear matrix maps

Ist Teil von

• Indagationes mathematicae, 2022-03, Vol.33 (2), p.334-356

Ort / Verlag

Amsterdam: Elsevier B.V

Erscheinungsjahr

2022

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In the paper (Hill, 1973) from 1973 R.D. Hill studied linear matrix maps L:ℂq×q→ℂn×n which map Hermitian matrices to Hermitian matrices, or equivalently, preserve adjoints, i.e., L(V∗)=L(V)∗, via representations of the form L(V)=∑k,l=1mHklAlVAk∗,V∈ℂq×q,for matrices A1,…,Am∈ℂn×q and continued his study of such representations in later work, sometimes with co-authors, to completely positive matrix maps and associated matrix reorderings. In this paper we expand the study of such representations, referred to as Hill representations here, in various directions. In particular, we describe which matrices A1,…,Am can appear in Hill representations (provided the number m is minimal) and determine the associated Hill matrix H=Hkl explicitly. Also, we describe how different Hill representations of L (again with m minimal) are related and investigate further the implication of ∗-linearity on the linear map L.