{"paper":{"title":"Grothendieck constant is norm of Strassen matrix multiplication tensor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Jinjie Zhang, Lek-Heng Lim, Shmuel Friedland","submitted_at":"2017-11-13T06:10:54Z","abstract_excerpt":"We show that two important quantities from two disparate areas of complexity theory --- Strassen's exponent of matrix multiplication $\\omega$ and Grothendieck's constant $K_G$ --- are intimately related. They are different measures of size for the same underlying object --- the matrix multiplication tensor, i.e., the $3$-tensor or bilinear operator $\\mu_{l,m,n} : \\mathbb{F}^{l \\times m} \\times \\mathbb{F}^{m \\times n} \\to \\mathbb{F}^{l \\times n}$, $(A,B) \\mapsto AB$ defined by matrix-matrix product over $\\mathbb{F} = \\mathbb{R}$ or $\\mathbb{C}$. It is well-known that Strassen's exponent of matr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04427","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"}