{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:6B62FPF6WLOI6HLUKRMFNM5UGA","short_pith_number":"pith:6B62FPF6","schema_version":"1.0","canonical_sha256":"f07da2bcbeb2dc8f1d74545856b3b43019b758fcf4b20cd687ede5a5cab15ba7","source":{"kind":"arxiv","id":"1806.10544","version":1},"attestation_state":"computed","paper":{"title":"Strong linearizations of rational matrices with polynomial part expressed in an orthogonal basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Froil\\'an M. Dopico, Mar\\'ia C. Quintana, Silvia Marcaida","submitted_at":"2018-06-27T16:02:26Z","abstract_excerpt":"We construct a new family of strong linearizations of rational matrices considering the polynomial part of them expressed in a basis that satisfies a three term recurrence relation. For this purpose, we combine the theory developed by Amparan et al., MIMS EPrint 2016.51, and the new linearizations of polynomial matrices introduced by Fa{\\ss}bender and Saltenberger, Linear Algebra Appl., 525 (2017). In addition, we present a detailed study of how to recover eigenvectors of a rational matrix from those of its linearizations in this family. We complete the paper by discussing how to extend the re"},"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":"1806.10544","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-27T16:02:26Z","cross_cats_sorted":[],"title_canon_sha256":"05f6eba53fa0d57323ba47b6af0d9cd7d5538007370863a633b4d6bd5c570c90","abstract_canon_sha256":"8b1f62da78ef70b36a76322bdf0816e28939faca76dd0bb64f82b7d4a2493337"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:12.062767Z","signature_b64":"cZvIWlltAqJBH4IAx9t30+IYO8QV6puwfCgJ4UNjmAzPIUF2RplU+d5i+/h9iy7UuAAJur6R87YZE0IghVzQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f07da2bcbeb2dc8f1d74545856b3b43019b758fcf4b20cd687ede5a5cab15ba7","last_reissued_at":"2026-05-18T00:12:12.061741Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:12.061741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong linearizations of rational matrices with polynomial part expressed in an orthogonal basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Froil\\'an M. Dopico, Mar\\'ia C. Quintana, Silvia Marcaida","submitted_at":"2018-06-27T16:02:26Z","abstract_excerpt":"We construct a new family of strong linearizations of rational matrices considering the polynomial part of them expressed in a basis that satisfies a three term recurrence relation. For this purpose, we combine the theory developed by Amparan et al., MIMS EPrint 2016.51, and the new linearizations of polynomial matrices introduced by Fa{\\ss}bender and Saltenberger, Linear Algebra Appl., 525 (2017). In addition, we present a detailed study of how to recover eigenvectors of a rational matrix from those of its linearizations in this family. We complete the paper by discussing how to extend the re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10544","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1806.10544","created_at":"2026-05-18T00:12:12.062108+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.10544v1","created_at":"2026-05-18T00:12:12.062108+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10544","created_at":"2026-05-18T00:12:12.062108+00:00"},{"alias_kind":"pith_short_12","alias_value":"6B62FPF6WLOI","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"6B62FPF6WLOI6HLU","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"6B62FPF6","created_at":"2026-05-18T12:32:08.215937+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/6B62FPF6WLOI6HLUKRMFNM5UGA","json":"https://pith.science/pith/6B62FPF6WLOI6HLUKRMFNM5UGA.json","graph_json":"https://pith.science/api/pith-number/6B62FPF6WLOI6HLUKRMFNM5UGA/graph.json","events_json":"https://pith.science/api/pith-number/6B62FPF6WLOI6HLUKRMFNM5UGA/events.json","paper":"https://pith.science/paper/6B62FPF6"},"agent_actions":{"view_html":"https://pith.science/pith/6B62FPF6WLOI6HLUKRMFNM5UGA","download_json":"https://pith.science/pith/6B62FPF6WLOI6HLUKRMFNM5UGA.json","view_paper":"https://pith.science/paper/6B62FPF6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.10544&json=true","fetch_graph":"https://pith.science/api/pith-number/6B62FPF6WLOI6HLUKRMFNM5UGA/graph.json","fetch_events":"https://pith.science/api/pith-number/6B62FPF6WLOI6HLUKRMFNM5UGA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6B62FPF6WLOI6HLUKRMFNM5UGA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6B62FPF6WLOI6HLUKRMFNM5UGA/action/storage_attestation","attest_author":"https://pith.science/pith/6B62FPF6WLOI6HLUKRMFNM5UGA/action/author_attestation","sign_citation":"https://pith.science/pith/6B62FPF6WLOI6HLUKRMFNM5UGA/action/citation_signature","submit_replication":"https://pith.science/pith/6B62FPF6WLOI6HLUKRMFNM5UGA/action/replication_record"}},"created_at":"2026-05-18T00:12:12.062108+00:00","updated_at":"2026-05-18T00:12:12.062108+00:00"}