{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ALINO6ESPROOPWO5RWJXHTIV75","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bbbe58230d0f4822aa3c74837e2d884c7a8d545ba848bf77f973bdc4cfbb37a0","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-19T12:36:47Z","title_canon_sha256":"017c0d50a6696ddc51cd1b46b468100f898ca6bafa959517ad30c4cdfe492db0"},"schema_version":"1.0","source":{"id":"1902.07024","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.07024","created_at":"2026-07-05T00:14:18Z"},{"alias_kind":"arxiv_version","alias_value":"1902.07024v2","created_at":"2026-07-05T00:14:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.07024","created_at":"2026-07-05T00:14:18Z"},{"alias_kind":"pith_short_12","alias_value":"ALINO6ESPROO","created_at":"2026-07-05T00:14:18Z"},{"alias_kind":"pith_short_16","alias_value":"ALINO6ESPROOPWO5","created_at":"2026-07-05T00:14:18Z"},{"alias_kind":"pith_short_8","alias_value":"ALINO6ES","created_at":"2026-07-05T00:14:18Z"}],"graph_snapshots":[{"event_id":"sha256:c04b2b0a1a1146199f6ef9e6287bdccbe150e13cdf1e56dab71e41d2a6a75d33","target":"graph","created_at":"2026-07-05T00:14:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1902.07024/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce the tensor similar transforation and propose the T-Jordan canonical form and its properties. The concept of T-minimal polynomial and T-characteristic polynomial are raised. As a special case, we present properties when two tensors commutes via the tensor T-product. The Cayley-Hamilton theorem also holds for tensor cases. Then we focus on the tensor decomposition theory. T-polar, T-LU, T-QR and T-Schur decomposition of tensors are obtained. When a F-square tensor is not invertible via the T-product, we give the T-group inverse and T-Drazin inverse which can be viewed","authors_text":"Liqun Qi, Yimin Wei, Yun Miao","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-19T12:36:47Z","title":"T-Jordan Canonical Form and T-Drazin Inverse based on the T-Product"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.07024","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:df8931ccb91eee9cab4644e8104f3d18a13afdd1e5ef7c90c105723d9705d04f","target":"record","created_at":"2026-07-05T00:14:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bbbe58230d0f4822aa3c74837e2d884c7a8d545ba848bf77f973bdc4cfbb37a0","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-19T12:36:47Z","title_canon_sha256":"017c0d50a6696ddc51cd1b46b468100f898ca6bafa959517ad30c4cdfe492db0"},"schema_version":"1.0","source":{"id":"1902.07024","kind":"arxiv","version":2}},"canonical_sha256":"02d0d778927c5ce7d9dd8d9373cd15ff7e49d6caba0edf5190a79866d749da2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02d0d778927c5ce7d9dd8d9373cd15ff7e49d6caba0edf5190a79866d749da2b","first_computed_at":"2026-07-05T00:14:18.996926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:14:18.996926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ki0JVi9gm/CiHCdc2o0LIEDb1U+2+r3H1tfKuZwtXYr8lph4eLA344aL+hx2/NF+zosK6WBOtXIhCZdpB2FJAw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:14:18.997350Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.07024","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df8931ccb91eee9cab4644e8104f3d18a13afdd1e5ef7c90c105723d9705d04f","sha256:c04b2b0a1a1146199f6ef9e6287bdccbe150e13cdf1e56dab71e41d2a6a75d33"],"state_sha256":"7b58d621c121b83144c8160bd95284c8f2ee773dd9241cbc39c01cbd2b7ec358"}