Geodesic
Variational principles for symplectic eigenvalues
Canadian mathematical bulletin, Tome 64 (2021) no. 3, pp. 553-559

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DOI

If A is a real $2n \times 2n$ positive definite matrix, then there exists a symplectic matrix M such that $M^TAM=\text {diag}(D, D),$ where D is a positive diagonal matrix with diagonal entries $d_1(A)\leqslant \cdots \leqslant d_n(A).$ We prove a maxmin principle for $d_k(A)$ akin to the classical Courant–Fisher–Weyl principle for Hermitian eigenvalues and use it to derive an analogue of the Weyl inequality $d_{i+j-1}(A+B)\geqslant d_i(A)+d_j(B).$
DOI : 10.4153/S0008439520000648
Mots-clés : Symplectic eigenvalues, maxmin principle, Weyl’s inequalities 
Bhatia, Rajendra; Jain, Tanvi. Variational principles for symplectic eigenvalues. Canadian mathematical bulletin, Tome 64 (2021) no. 3, pp. 553-559. doi: 10.4153/S0008439520000648
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     title = {Variational principles for symplectic eigenvalues},
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     doi = {10.4153/S0008439520000648},
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