{"paper":{"title":"Analogs of Cramer's rule for the least squares solutions of some matrix equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ivan Kyrchei","submitted_at":"2011-08-29T11:07:56Z","abstract_excerpt":"The least squares solutions with the minimum norm of the matrix equations ${\\rm {\\bf A}}{\\rm {\\bf X}} = {\\rm {\\bf B}}$, ${\\rm {\\bf X}}{\\rm {\\bf A}} = {\\rm {\\bf B}}$ and ${\\rm {\\bf A}}{\\rm {\\bf X}}{\\rm {\\bf B}} ={\\rm {\\bf D}} $ are considered in this paper. We use the determinantal representations of the Moore - Penrose inverse obtained earlier by the author and get analogs of the Cramer rule for the least squares solutions of these matrix equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5522","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":""},"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"}