{"paper":{"title":"An Algebraic Approach to Non-Orthogonal General Joint Block Diagonalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Chengyu Liu, Yunfeng Cai","submitted_at":"2016-07-04T01:19:28Z","abstract_excerpt":"The exact/approximate non-orthogonal general joint block diagonalization ({\\sc nogjbd}) problem of a given real matrix set $\\mathcal{A}=\\{A_i\\}_{i=1}^m$ is to find a nonsingular matrix $W\\in\\mathbb{R}^{n\\times n}$ (diagonalizer) such that $W^T A_i W$ for $i=1,2,\\dots, m$ are all exactly/approximately block diagonal matrices with the same diagonal block structure and with as many diagonal blocks as possible. In this paper, we show that a solution to the exact/approximate {\\sc nogjbd} problem can be obtained by finding the exact/approximate solutions to the system of linear equations $A_iZ=Z^TA_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00716","kind":"arxiv","version":3},"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"}