{"paper":{"title":"Comment on `The tan {\\theta} theorem with relaxed conditions', by Y. Nakatsukasa","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","physics.comp-ph"],"primary_cat":"math.SP","authors_text":"Alexander K. Motovilov","submitted_at":"2012-04-19T19:27:24Z","abstract_excerpt":"We show that in case of the spectral norm, one of the main results of the recent paper \"The tan {\\theta} theorem with relaxed conditions\", by Yuji Nakatsukasa, published in Linear Algebra and its Applications is a corollary of the tan {\\theta} theorem proven in [V.Kostrykin, K.A.Makarov, and A.K.Motovilov, On the existence of solutions to the operator Riccati equation and the tan {\\theta} theorem, IEOT 51 (2005), 121-140]. We also give an alternative finite-dimensional matrix formulation of another tan {\\theta} theorem proven in [S.Albeverio and A.K.Motovilov, The a priori tan {\\theta} theorem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4441","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"}