Open AccessWeak Log-majorization of Unital Trace-preserving Completely Positive Maps
Author(s) -
Pan Shun Lau,
Tin-Yau Tam
Publication year - 2019
Publication title -
the electronic journal of linear algebra
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.447
H-Index - 31
eISSN - 1537-9582
pISSN - 1081-3810
DOI - 10.13001/ela.2019.5177
Subject(s) - majorization , mathematics , trace (psycholinguistics) , unital , combinatorics , positive definite matrix , matrix (chemical analysis) , pure mathematics , discrete mathematics , algebra over a field , philosophy , eigenvalues and eigenvectors , linguistics , physics , quantum mechanics , materials science , composite material
Let Φ : Mn → Mn be a unital trace preserving completely positive map and A ∈ Mn be a positive definite matrix. Weak log-majorization and weak majorization between Φ(A) and A are studied. Determinantal inequalities between Φ(A) and A are obtained as a consequence. By considering special classes of unital trace preserving completely positive map, some known matrix inequalities such as Fischer’s inequality are rediscovered. An affirmative answer to a question of Tam and Zhang in 2019 is given.