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The function $f[A(t)]$ is supposed to be an operator acting on the same space as the operator $A(t)$. We use the basis which diagonalizes A(t), i.e., $A_{i j}=\\lambda_i \\delta_{i j}$, and obtain $[\\frac{\\partial f[A(t)]}{\\partial t}]_{i j}=[\\frac{\\partial A}{\\partial t}]_ {i j}\\frac{f(\\lambda_j) - f(\\lambda_i)} {\\lambda_j - \\lambda_i}$. In addition to this, we show that further"},"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":"cond-mat/9906173","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1999-06-11T16:55:11Z","cross_cats_sorted":[],"title_canon_sha256":"ccfb664f45af2800e107518387ce266ebadddcf574e37a79bdcb25527905b5f3","abstract_canon_sha256":"4208fcbe84a186dd97c0a5df12a13a4df8f0a5b7a1a82b292f5fec092300912b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:28.703090Z","signature_b64":"9SmnsHYMOk/wgOlESRZNfgijjZgZWLKfKo6CQ4QltAcVGzUN6z83k7L2hW6d4w+XS7f6qQ8aWY7tAIoob4Z9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"511a6736fcd06cc488d5b52599c96945bf6fba174dd61178d5a7919375675aa8","last_reissued_at":"2026-05-18T01:39:28.702433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:28.702433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functions of linear operators: Parameter differentiation","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Argentina), Astronomia y Fisica, Brazil), Ciudad Universitaria, Constantino Tsallis (Centro Brasileiro de Pesquisas Fisicas, Cordoba, Domingo Prato (Facultad de Matematica, Rio de Janeiro-RJ, Universidad Nacional de Cordoba","submitted_at":"1999-06-11T16:55:11Z","abstract_excerpt":"We derive a useful expression for the matrix elements $[\\frac{\\partial f[A(t)]}{\\partial t}]_{i j}$ of the derivative of a function $f[A(t)]$ of a diagonalizable linear operator $A(t)$ with respect to the parameter $t$. The function $f[A(t)]$ is supposed to be an operator acting on the same space as the operator $A(t)$. We use the basis which diagonalizes A(t), i.e., $A_{i j}=\\lambda_i \\delta_{i j}$, and obtain $[\\frac{\\partial f[A(t)]}{\\partial t}]_{i j}=[\\frac{\\partial A}{\\partial t}]_ {i j}\\frac{f(\\lambda_j) - f(\\lambda_i)} {\\lambda_j - \\lambda_i}$. 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