{"paper":{"title":"On a class of non-Hermitian matrices with positive definite Schur complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Carsten Trunk, Francisco Mart\\'inez Per\\'ia, Juan Ignacio Giribet, Thomas Berger","submitted_at":"2018-07-23T13:17:25Z","abstract_excerpt":"Given a positive definite matrix $A\\in \\mathbb{C}^{n\\times n}$ and a Hermitian matrix $D\\in \\mathbb{C}^{m\\times m}$, we characterize under which conditions there exists a strictly contractive matrix $K\\in \\mathbb{C}^{n\\times m}$ such that the non-Hermitian block-matrix \\[ \\left[ \\begin{array}{cc} A & -AK \\\\ K^*A & D \\end{array} \\right] \\] has a positive definite Schur complement with respect to its submatrix~$A$. Additionally, we show that~$K$ can be chosen such that diagonalizability of the block-matrix is guaranteed and we compute its spectrum. Moreover, we show a connection to the recently "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08591","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}