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This paper proposes a unified matrix model $$\\bold{\\bbom}=(\\bbZ\\bbU_2\\bbU_2^T\\bbZ^T)^{-1}\\bbZ\\bbU_1\\bbU_1^T\\bbZ^T,$$ where $\\bbU_1$ and $\\bbU_2$ are isometric with dimensions $N\\times N_1$ and $N\\times (N-N_2)$ respectively such that $\\bbU_1^T\\bbU_1=\\bbI_{N_1}$, $\\bbU_2^T\\bbU_2=\\bbI_{N-N_2}$ and $\\bbU_1^T\\bbU_2=0$. Moreover, $\\bbU_1$ and $\\bbU_2$ (random or non-random) are independent of $\\bbZ_{M_1"},"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":"1606.04417","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-06-14T15:16:13Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"403ea0d0111b58b0e839201f7aa5002e01e680ad853471277995a4bf53a625e4","abstract_canon_sha256":"3f6217dc4c1d86a3d161d6a80bdbdb69d3131d8ee4b0309ed21b0de19f2f7ea4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:01.258213Z","signature_b64":"Nz9187Pl4C+TtU8EeI5ppgYAPT/1o+gHnTaGpwSFzsCiOQh6XqxTxtlP0lh/hNwWS7MVXKeZZSPDyPq0e/kCDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7965caa8c01d142af07469a48e4d2245636ba36504c4dc793fff89a03c5e759","last_reissued_at":"2026-05-18T01:12:01.257859Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:01.257859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A unified matrix model including both CCA and F matrices in multivariate analysis: the largest eigenvalue and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Guangming Pan, Qing Yang, Xiao Han","submitted_at":"2016-06-14T15:16:13Z","abstract_excerpt":"Let $\\bbZ_{M_1\\times N}=\\bbT^{\\frac{1}{2}}\\bbX$ where $(\\bbT^{\\frac{1}{2}})^2=\\bbT$ is a positive definite matrix and $\\bbX$ consists of independent random variables with mean zero and variance one. This paper proposes a unified matrix model $$\\bold{\\bbom}=(\\bbZ\\bbU_2\\bbU_2^T\\bbZ^T)^{-1}\\bbZ\\bbU_1\\bbU_1^T\\bbZ^T,$$ where $\\bbU_1$ and $\\bbU_2$ are isometric with dimensions $N\\times N_1$ and $N\\times (N-N_2)$ respectively such that $\\bbU_1^T\\bbU_1=\\bbI_{N_1}$, $\\bbU_2^T\\bbU_2=\\bbI_{N-N_2}$ and $\\bbU_1^T\\bbU_2=0$. 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