{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:LGG5U4ZASFCKDMXLQLZSEKPPB3","short_pith_number":"pith:LGG5U4ZA","schema_version":"1.0","canonical_sha256":"598dda73209144a1b2eb82f32229ef0ef3435372b0bc3df65cc2d7a27e17692d","source":{"kind":"arxiv","id":"1008.2923","version":4},"attestation_state":"computed","paper":{"title":"A Spectral Theory for Tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Ahmed Elgammal, Edinah K. Gnang, Vladimir Retakh","submitted_at":"2010-08-17T16:08:35Z","abstract_excerpt":"In this paper we propose a general spectral theory for tensors. Our proposed factorization decomposes a tensor into a product of orthogonal and scaling tensors. At the same time, our factorization yields an expansion of a tensor as a summation of outer products of lower order tensors . Our proposed factorization shows the relationship between the eigen-objects and the generalised characteristic polynomials. Our framework is based on a consistent multilinear algebra which explains how to generalise the notion of matrix hermicity, matrix transpose, and most importantly the notion of orthogonalit"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1008.2923","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-08-17T16:08:35Z","cross_cats_sorted":[],"title_canon_sha256":"1dc99beeee76cbdd1aaf4328f0d7cb5fad04f7f952f2121bdb7504c3927e9002","abstract_canon_sha256":"becff9d11764abcc701273fba787dc5ed67b28f4501ba3f6b7e8bb2cb668e6bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:01.012684Z","signature_b64":"Zp7aFy/cpksTt2ZIUZ7KnX80AxtkQzzbBao7Y1XXWtOTZilHgvj16SUwUO7Ol4p3g0ZpgGeXvIIhhoeethnrDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"598dda73209144a1b2eb82f32229ef0ef3435372b0bc3df65cc2d7a27e17692d","last_reissued_at":"2026-05-18T04:02:01.012021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:01.012021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Spectral Theory for Tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Ahmed Elgammal, Edinah K. Gnang, Vladimir Retakh","submitted_at":"2010-08-17T16:08:35Z","abstract_excerpt":"In this paper we propose a general spectral theory for tensors. Our proposed factorization decomposes a tensor into a product of orthogonal and scaling tensors. At the same time, our factorization yields an expansion of a tensor as a summation of outer products of lower order tensors . Our proposed factorization shows the relationship between the eigen-objects and the generalised characteristic polynomials. Our framework is based on a consistent multilinear algebra which explains how to generalise the notion of matrix hermicity, matrix transpose, and most importantly the notion of orthogonalit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2923","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1008.2923","created_at":"2026-05-18T04:02:01.012149+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.2923v4","created_at":"2026-05-18T04:02:01.012149+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2923","created_at":"2026-05-18T04:02:01.012149+00:00"},{"alias_kind":"pith_short_12","alias_value":"LGG5U4ZASFCK","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"LGG5U4ZASFCKDMXL","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"LGG5U4ZA","created_at":"2026-05-18T12:26:10.704358+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LGG5U4ZASFCKDMXLQLZSEKPPB3","json":"https://pith.science/pith/LGG5U4ZASFCKDMXLQLZSEKPPB3.json","graph_json":"https://pith.science/api/pith-number/LGG5U4ZASFCKDMXLQLZSEKPPB3/graph.json","events_json":"https://pith.science/api/pith-number/LGG5U4ZASFCKDMXLQLZSEKPPB3/events.json","paper":"https://pith.science/paper/LGG5U4ZA"},"agent_actions":{"view_html":"https://pith.science/pith/LGG5U4ZASFCKDMXLQLZSEKPPB3","download_json":"https://pith.science/pith/LGG5U4ZASFCKDMXLQLZSEKPPB3.json","view_paper":"https://pith.science/paper/LGG5U4ZA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.2923&json=true","fetch_graph":"https://pith.science/api/pith-number/LGG5U4ZASFCKDMXLQLZSEKPPB3/graph.json","fetch_events":"https://pith.science/api/pith-number/LGG5U4ZASFCKDMXLQLZSEKPPB3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LGG5U4ZASFCKDMXLQLZSEKPPB3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LGG5U4ZASFCKDMXLQLZSEKPPB3/action/storage_attestation","attest_author":"https://pith.science/pith/LGG5U4ZASFCKDMXLQLZSEKPPB3/action/author_attestation","sign_citation":"https://pith.science/pith/LGG5U4ZASFCKDMXLQLZSEKPPB3/action/citation_signature","submit_replication":"https://pith.science/pith/LGG5U4ZASFCKDMXLQLZSEKPPB3/action/replication_record"}},"created_at":"2026-05-18T04:02:01.012149+00:00","updated_at":"2026-05-18T04:02:01.012149+00:00"}