{"paper":{"title":"Embeddings of Schatten Norms with Applications to Data Streams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Yi Li","submitted_at":"2017-02-18T15:47:39Z","abstract_excerpt":"Given an $n \\times d$ matrix $A$, its Schatten-$p$ norm, $p \\geq 1$, is defined as $\\|A\\|_p = \\left (\\sum_{i=1}^{\\textrm{rank}(A)}\\sigma_i(A)^p \\right )^{1/p}$, where $\\sigma_i(A)$ is the $i$-th largest singular value of $A$. These norms have been studied in functional analysis in the context of non-commutative $\\ell_p$-spaces, and recently in data stream and linear sketching models of computation. Basic questions on the relations between these norms, such as their embeddability, are still open. Specifically, given a set of matrices $A^1, \\ldots, A^{\\operatorname{poly}(nd)} \\in \\mathbb{R}^{n \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05626","kind":"arxiv","version":1},"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"}