Fischer Type Log-Majorization of Singular Values on Partitioned Positive Semidefinite Matrices

In this paper, we establish a Fischer type log-majorization of singular values on partitioned positive semidefinite matrices, which generalizes the classical Fischer's inequality. Meanwhile, some related and new inequalities are also obtained.

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

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.