{"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 $[\\frac{\\partial f[A(t)]}{\\partial t}]_{i j}=[\\frac{\\partial A}{\\partial t}]_ {i j}\\frac{f(\\lambda_j) - f(\\lambda_i)} {\\lambda_j - \\lambda_i}$. In addition to this, we show that further"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9906173","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"}