{"paper":{"title":"Solving General Joint Block Diagonalization Problem via Linearly Independent Eigenvectors of a Matrix Polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Decai Shi, Guanghui Cheng, Yunfeng Cai","submitted_at":"2017-04-19T08:08:51Z","abstract_excerpt":"In this paper, we consider the exact/approximate general joint block diagonalization (GJBD) problem of a matrix set $\\{A_i\\}_{i=0}^p$ ($p\\ge 1$), where a nonsingular matrix $W$ (often referred to as diagonalizer) needs to be found such that the matrices $W^{H}A_iW$'s are all exactly/approximately block diagonal matrices with as many diagonal blocks as possible. We show that the diagonalizer of the exact GJBD problem can be given by $W=[x_1, x_2, \\dots, x_n]\\Pi$, where $\\Pi$ is a permutation matrix, $x_i$'s are eigenvectors of the matrix polynomial $P(\\lambda)=\\sum_{i=0}^p\\lambda^i A_i$, satisf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05642","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"}