{"paper":{"title":"On a Class of Matrix Pencils and $\\ell$-ifications Equivalent to a Given Matrix Polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dario A. Bini, Leonardo Robol","submitted_at":"2014-06-04T12:42:24Z","abstract_excerpt":"A new class of linearizations and $\\ell$-ifications for $m\\times m$ matrix polynomials $P(x)$ of degree $n$ is proposed. The $\\ell$-ifications in this class have the form $A(x) = D(x) + (e\\otimes I_m) W(x)$ where $D$ is a block diagonal matrix polynomial with blocks $B_i(x)$ of size $m$, $W$ is an $m\\times qm$ matrix polynomial and $e=(1,\\ldots,1)^t\\in\\mathbb C^q$, for a suitable integer $q$. The blocks $B_i(x)$ can be chosen a priori, subjected to some restrictions. Under additional assumptions on the blocks $B_i(x)$ the matrix polynomial $A(x)$ is a strong $\\ell$-ification, i.e., the reverse"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1025","kind":"arxiv","version":4},"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"}