{"paper":{"title":"Dynamics of two by two symmetric matrices of trace zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Arijit Mukherjee","submitted_at":"2024-03-17T12:57:15Z","abstract_excerpt":"In this paper, we describe the entire structure of the vector space $Sym_2^0$ of all symmetric matrices of size $2$ having trace zero. This is motivated by the geometrical interpretation of any arbitrary element of $Sym_2^0$. We further study the orbits and stable sets of these elements. As an application of the obtained structure of $Sym_2^0$, we obtain the symmetric matrices of size $2$, trace of whose product with any trace zero symmetric matrix is zero. Finally some well known trigonometric formulas are interpreted geometrically incorporating the anatomy of $Sym_2^0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.11201","kind":"arxiv","version":1},"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/2403.11201/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"}