{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZH7BZWSHMWHJRM4GQHUOWQ6XQQ","short_pith_number":"pith:ZH7BZWSH","schema_version":"1.0","canonical_sha256":"c9fe1cda47658e98b38681e8eb43d784316ecffbfd35dbb9ceb12d0d9fd9fd58","source":{"kind":"arxiv","id":"1712.01070","version":1},"attestation_state":"computed","paper":{"title":"The normalized numerical range and the Davis-Wielandt shell","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"Brian Lins, Ilya M. Spitkovsky, Siyu Zhong","submitted_at":"2017-12-04T13:42:10Z","abstract_excerpt":"For a given $n$-by-$n$ matrix $A$, its {\\em normalized numerical range} $F_N(A)$ is defined as the range of the function $f_{N,A}\\colon x\\mapsto (x^*Ax)/(\\norm{Ax}\\cdot\\norm{x})$ on the complement of $\\ker A$. We provide an explicit description of this set for the case when $A$ is normal or $n=2$. This extension of earlier results for particular cases of $2$-by-$2$ matrices (by Gevorgyan) and essentially Hermitian matrices of arbitrary size (by A. Stoica and one of the authors) was achieved due to the fresh point of view at $F_N(A)$ as the image of the Davis-Wielandt shell $\\JNR(A)$ under a ce"},"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":"1712.01070","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-12-04T13:42:10Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"9fc0b9bbae6672b1907989c100cdcff03305c81f26cfa9fb63501fa51896ef9e","abstract_canon_sha256":"03bd71896a515435200955020bf7d332b207b9b02dcd4679b0eea0bfe830f1f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:59.608469Z","signature_b64":"+vWU7s2WdjbBzbDCKA0gyLzHecB/7pc11xAq8UlMSWuesglBAArN/7qCJJWGkdtmxQxXJOUqc1s/UOyOIeKMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9fe1cda47658e98b38681e8eb43d784316ecffbfd35dbb9ceb12d0d9fd9fd58","last_reissued_at":"2026-05-18T00:28:59.608072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:59.608072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The normalized numerical range and the Davis-Wielandt shell","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"Brian Lins, Ilya M. Spitkovsky, Siyu Zhong","submitted_at":"2017-12-04T13:42:10Z","abstract_excerpt":"For a given $n$-by-$n$ matrix $A$, its {\\em normalized numerical range} $F_N(A)$ is defined as the range of the function $f_{N,A}\\colon x\\mapsto (x^*Ax)/(\\norm{Ax}\\cdot\\norm{x})$ on the complement of $\\ker A$. We provide an explicit description of this set for the case when $A$ is normal or $n=2$. This extension of earlier results for particular cases of $2$-by-$2$ matrices (by Gevorgyan) and essentially Hermitian matrices of arbitrary size (by A. Stoica and one of the authors) was achieved due to the fresh point of view at $F_N(A)$ as the image of the Davis-Wielandt shell $\\JNR(A)$ under a ce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01070","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":"1712.01070","created_at":"2026-05-18T00:28:59.608138+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.01070v1","created_at":"2026-05-18T00:28:59.608138+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.01070","created_at":"2026-05-18T00:28:59.608138+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZH7BZWSHMWHJ","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZH7BZWSHMWHJRM4G","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZH7BZWSH","created_at":"2026-05-18T12:31:59.375834+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/ZH7BZWSHMWHJRM4GQHUOWQ6XQQ","json":"https://pith.science/pith/ZH7BZWSHMWHJRM4GQHUOWQ6XQQ.json","graph_json":"https://pith.science/api/pith-number/ZH7BZWSHMWHJRM4GQHUOWQ6XQQ/graph.json","events_json":"https://pith.science/api/pith-number/ZH7BZWSHMWHJRM4GQHUOWQ6XQQ/events.json","paper":"https://pith.science/paper/ZH7BZWSH"},"agent_actions":{"view_html":"https://pith.science/pith/ZH7BZWSHMWHJRM4GQHUOWQ6XQQ","download_json":"https://pith.science/pith/ZH7BZWSHMWHJRM4GQHUOWQ6XQQ.json","view_paper":"https://pith.science/paper/ZH7BZWSH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.01070&json=true","fetch_graph":"https://pith.science/api/pith-number/ZH7BZWSHMWHJRM4GQHUOWQ6XQQ/graph.json","fetch_events":"https://pith.science/api/pith-number/ZH7BZWSHMWHJRM4GQHUOWQ6XQQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZH7BZWSHMWHJRM4GQHUOWQ6XQQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZH7BZWSHMWHJRM4GQHUOWQ6XQQ/action/storage_attestation","attest_author":"https://pith.science/pith/ZH7BZWSHMWHJRM4GQHUOWQ6XQQ/action/author_attestation","sign_citation":"https://pith.science/pith/ZH7BZWSHMWHJRM4GQHUOWQ6XQQ/action/citation_signature","submit_replication":"https://pith.science/pith/ZH7BZWSHMWHJRM4GQHUOWQ6XQQ/action/replication_record"}},"created_at":"2026-05-18T00:28:59.608138+00:00","updated_at":"2026-05-18T00:28:59.608138+00:00"}