{"paper":{"title":"Linear rank preservers of tensor products of rank one matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.FA","authors_text":"Nung-sing Sze, Shiyu Shi, Zejun Huang","submitted_at":"2015-09-02T01:58:04Z","abstract_excerpt":"Let $n_1,\\ldots,n_k $ be integers larger than or equal to 2. We characterize linear maps $\\phi: M_{n_1\\cdots n_k}\\rightarrow M_{n_1\\cdots n_k}$ such that $${\\mathrm rank}\\,(\\phi(A_1\\otimes \\cdots \\otimes A_k))=1\\quad\\hbox{whenever}\\quad{\\mathrm rank}\\, (A_1\\otimes \\cdots \\otimes A_k)=1 \\quad \\hbox{for all}\\quad A_i \\in M_{n_i},\\, i = 1,\\dots,k.$$ Applying this result, we extend two recent results on linear maps that preserving the rank of special classes of matrices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00541","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"}