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We find the eigen-pairs of the matrices $R_n$."},"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":"1101.5788","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-01-30T17:39:33Z","cross_cats_sorted":[],"title_canon_sha256":"f5600b97412e613242d322184400671c1416609ab676921dfa1f7f17b4a9ba4d","abstract_canon_sha256":"643091694ecee18d382163f8d16b16143d54bfdc4e5271975bdd917310a30c83"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:24.811600Z","signature_b64":"tIOyW01bNxU7daGoZ1oIlLrXs4dcj8gdtJxJDyGnE/eui4DHjsGWwX5v8emYP5zmnA46pYJ5qxUEQtThs+ayDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2511212b444c18a5e51551e206e11a415f02e4db3442fffa32646c4e92e5fe44","last_reissued_at":"2026-05-18T04:30:24.810831Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:24.810831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Eigen-Problem for Some Special Near-Toeplitz Centro-Skew Tridiagonal Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Antonio Behn, Irvin R. Hentzel, Kenneth R. Driessel","submitted_at":"2011-01-30T17:39:33Z","abstract_excerpt":"Let $n\\ge 2$ be an integer. Let $R_n$ denote the $n\\times n$ tridiagonal matrix with $-1$'s on the sub-diagonal, $1$'s on the super-diagonal, $-1$ in the $(1,1)$ entry, $1$ in the $(n,n)$ entry and zeros elsewhere. 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