The Horn cone associated with symplectic eigenvalues. (English) Zbl 1529.15011
Summary: In this note, we show that the Horn cone associated with symplectic eigenvalues admits the same inequalities as the classical Horn cone, except that the equality corresponding to \(\mathrm{Tr}(C)=\mathrm{Tr}(A)+\mathrm{Tr}(B)\) is replaced by the inequality corresponding to \(\mathrm{Tr}(C)\geq \mathrm{Tr}(A)+\mathrm{Tr}(B)\).
MSC:
| 15A42 | Inequalities involving eigenvalues and eigenvectors |
| 15A15 | Determinants, permanents, traces, other special matrix functions |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
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