{"paper":{"title":"On a family of Laurent polynomials generated by 2x2 matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Victor Katsnelson","submitted_at":"2015-07-22T08:43:53Z","abstract_excerpt":"To a $2\\times2$ matrix $G$ with complex entries, we relate the sequence of Laurent polynomial $L_n(z,G)=\\tr \\big(G\\big[\\begin{smallmatrix}z&0\\\\ 0&z^{-1}\\end{smallmatrix}\\big]G^{\\ast}\\big)^n$. It turns out that for each \\(n\\), the family $\\big\\{L_n(z,G)\\big\\}_G$, where $G$ runs over the set of all $2\\times2$ matrices, is a three-parametric family. A natural parametrization of this family is found. The polynomial $L_n(z,G)$ is expressed in terms of these parameters and the Chebyshev polynomial $T_n$. The zero set of the polynomial $L_n(z,G)$ is described."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06101","kind":"arxiv","version":2},"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"}