{"paper":{"title":"Unconstrained representation of orthogonal matrices with application to common principle components","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.AP","stat.CO"],"primary_cat":"stat.ME","authors_text":"Antonio Punzo, Luca Bagnato","submitted_at":"2019-06-03T05:58:54Z","abstract_excerpt":"Many statistical problems involve the estimation of a $\\left(d\\times d\\right)$ orthogonal matrix $\\textbf{Q}$. Such an estimation is often challenging due to the orthonormality constraints on $\\textbf{Q}$. To cope with this problem, we propose a very simple decomposition for orthogonal matrices which we abbreviate as PLR decomposition. It produces a one-to-one correspondence between $\\textbf{Q}$ and a $\\left(d\\times d\\right)$ unit lower triangular matrix $\\textbf{L}$ whose $d\\left(d-1\\right)/2$ entries below the diagonal are unconstrained real values. Once the decomposition is applied, regardl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00587","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"}