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Among other determinantal inequalities, it is proved $\\det(I_n+T^*T)\\ge \\det(I_r+X^*X)\\cdot \\det(I_{n-r}+Z^*Z)$ with equality holds if and only if $Y=0$."},"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":"1410.5143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-20T02:48:24Z","cross_cats_sorted":[],"title_canon_sha256":"8b0a4cdb7eb217a4d8329a02e5e2edcc02f66b540c7943536651b49d43ac5bb8","abstract_canon_sha256":"a4292b7513571afc42dd2fcd187e16937bde7f0afabc7bf3081308092df4fceb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:46.770436Z","signature_b64":"ngtRVHXfGe1WJYcvMSUq8U/4Uf4GoVWfWMwgxLXqCKtI2H5ce6uqG/79om3rdZISJ717vtDn9vUB1l7vFdoTAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab6824717c7ab1bcb0ae3966852644ee93862876aec92509c51905656b8087b4","last_reissued_at":"2026-05-18T02:39:46.769827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:46.769827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Determinantal inequalities for block triangular matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Minghua Lin","submitted_at":"2014-10-20T02:48:24Z","abstract_excerpt":"Let $T=\\begin{bmatrix} X &Y\\\\ 0 & Z\\end{bmatrix}$ be an $n$-square matrix, where $X, Z$ are $r$-square and $(n-r)$-square, respectively. 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