Weak Log-majorization of Unital Trace-preserving Completely Positive Maps | Zendy

Pan Shun Lau | Zendy; Tin-Yau Tam | Zendy

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Weak Log-majorization of Unital Trace-preserving Completely Positive Maps

Author(s) -

Pan Shun Lau,

Tin-Yau Tam

Publication year - 2019

Publication title -

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.

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