{"paper":{"title":"Arveson extreme points span free spectrahedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Eric Evert, J. William Helton","submitted_at":"2018-06-23T23:42:44Z","abstract_excerpt":"Let $ SM_n(\\mathbb{R})^g$ denote $g$-tuples of $n \\times n$ real symmetric matrices. Given tuples $X=(X_1, \\dots, X_g) \\in SM_{n_1}(\\mathbb{R})^g$ and $Y=(Y_1, \\dots, Y_g) \\in SM_{n_2}(\\mathbb{R})^g$, a matrix convex combination of $X$ and $Y$ is a sum of the form \\[ V_1^* XV_1+V_2^* Y V_2 \\quad \\quad \\quad V_1^* V_1+V_2^* V_2=I_n \\] where $V_1:\\mathbb{R}^n \\to \\mathbb{R}^{n_1}$ and $V_2:\\mathbb{R}^n \\to \\mathbb{R}^{n_2}$ are contractions. Matrix convex sets are sets which are closed under matrix convex combinations. A key feature of matrix convex combinations is that the $g$-tuples $X, Y$, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09053","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1806.09053/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}