Abstract
In this article, two inequalities related to 2times 2 block sector partial transpose matrices are proved, and we also present a unitarily invariant norm inequality for the Hua matrix which is sharper than an existing result.
Highlights
We denote by Mn the set of n × n complex matrices
A positive semidefinite matrix A will be expressed as A ≥ 0
It is natural to extend the results for PPT matrices to SPT matrices
Summary
Mn(Mk) is the set of n × n block matrices with each block in Mk. The n × n identity matrix is denoted by In. We use · for an arbitrary unitarily invariant norm. A positive semidefinite matrix A will be expressed as A ≥ 0. Sn(A), are the eigenvalues of the positive semidefinite matrix |A| = (A∗A)1/2, arranged in decreasing order and repeated according to multiplicity as s1(A) ≥ s2(A) ≥ · · · ≥ sn(A). It is natural to extend the results for PPT matrices to SPT matrices.
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