{"paper":{"title":"Nonsurjective maps between rectangular matrix spaces preserving disjointness, triple products, or norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.RA","authors_text":"Chi-Kwong Li, Ming-Cheng Tsai, Ngai-Ching Wong, Ya-Shu Wang","submitted_at":"2019-03-05T23:30:10Z","abstract_excerpt":"Let $M_{m,n}$ be the space of $m\\times n$ real or complex rectangular matrices. Two matrices $A, B \\in M_{m,n}$ are disjoint if $A^*B = 0_n$ and $AB^* = 0_m$. In this paper, a characterization is given for linear maps $\\Phi: M_{m,n} \\rightarrow M_{r,s}$ sending disjoint matrix pairs to disjoint matrix pairs, i.e., $A, B \\in M_{m,n}$ are disjoint ensures that $\\Phi(A), \\Phi(B) \\in M_{r,s}$ are disjoint. More precisely, it is shown that $\\Phi$ preserves disjointness if and only if $\\Phi$ is of the form $$\\Phi(A) = U\\begin{pmatrix} A \\otimes Q_1 & 0 & 0 \\cr 0 & A^t \\otimes Q_2 & 0 \\cr 0 & 0 & 0 \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03456","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"}