{"paper":{"title":"Algebraic Linearizations of Matrix Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Eunice Y. S. Chan, J. Rafael Sendra, Juana Sendra, Laureano Gonzalez-Vega, Robert M. Corless","submitted_at":"2018-05-29T16:55:49Z","abstract_excerpt":"We show how to construct linearizations of matrix polynomials $z\\mathbf{a}(z)\\mathbf{d}_0 + \\mathbf{c}_0$, $\\mathbf{a}(z)\\mathbf{b}(z)$, $\\mathbf{a}(z) + \\mathbf{b}(z)$ (when $\\mathrm{deg}\\left(\\mathbf{b}(z)\\right) < \\mathrm{deg}\\left(\\mathbf{a}(z)\\right)$), and $z\\mathbf{a}(z)\\mathbf{d}_0\\mathbf{b}(z) + \\mathbf{c_0}$ from linearizations of the component parts, $\\mathbf{a}(z)$ and $\\mathbf{b}(z)$. This allows the extension to matrix polynomials of a new companion matrix construction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11580","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"}