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Abstract Let M = [ A X X ⁎ B ] ∈ C 2 n × 2 n be positive semi-definite 2 × 2 block matrix, where A , B… Click to show full abstract
Abstract Let M = [ A X X ⁎ B ] ∈ C 2 n × 2 n be positive semi-definite 2 × 2 block matrix, where A , B , X ∈ C n × n . A characterization for the matrix M with A + B = k I to be positive partial transpose is given in terms of its spectral norm. Using this result, a counter-example is constructed for the conjecture that ‖ M ‖ ≤ ‖ A + B ‖ when X is normal for all unitarily invariant norms.
Keywords:
semi definite;
positive semi;
definite block;
norm;
block matrices
Journal Title: Linear Algebra and its Applications
Year Published: 2018
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Journal Title: Linear Algebra and its Applications
Year Published: 2018
Link to full text (if available)
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recommendations!