Dias, C. NunoGosson, A. MauricePrata, N. João2025-11-112025-11-112024Dias, N. C., de Gosson, M. A., & Prata, J. N. (2024). On orthogonal projections of symplectic balls. Comptes Rendus. Mathématique, 362(G3), 217-227.http://hdl.handle.net/10400.26/59608We study the orthogonal projections of symplectic balls in R2n on complex subspaces. In particular we show that these projections are themselves symplectic balls under a certain complexity assumption. Our main result is a refinement of a recent very interesting result of Abbondandolo and Matveyev extending the linear version of Gromov’s non-squeezing theorem. We use a conceptually simpler approachwhere the Schur complement of a matrix plays a central role. An application to the partial traces of density matrices is given.engSymplectic ballorthogonal projectionGromov’s non-squeezing theoremreview article10.5802/crmath.542