{"paper":{"title":"Maximum vanishing subspace problem, CAT(0)-space relaxation, and block-triangularization of partitioned matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.OC","authors_text":"Hiroshi Hirai, Masaki Hamada","submitted_at":"2017-05-05T01:50:54Z","abstract_excerpt":"In this paper, we address the following algebraic generalization of the bipartite stable set problem. We are given a block-structured matrix (partitioned matrix) $A = (A_{\\alpha \\beta})$, where $A_{\\alpha \\beta}$ is an $m_{\\alpha}$ by $n_{\\beta}$ matrix over field ${\\bf F}$ for $\\alpha=1,2,\\ldots,\\mu$ and $\\beta = 1,2,\\ldots,\\nu$. The maximum vanishing subspace problem (MVSP) is to maximize $\\sum_{\\alpha} \\dim X_{\\alpha} + \\sum_{\\beta} \\dim Y_{\\beta}$ over vector subspaces $X_{\\alpha} \\subseteq {\\bf F}^{m_{\\alpha}}$ for $\\alpha=1,2,\\ldots,\\mu$ and $Y_{\\beta} \\subseteq {\\bf F}^{n_{\\beta}}$ for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02060","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"}