{"paper":{"title":"A functional calculus and the complex conjugate of a matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Olavi Nevanlinna","submitted_at":"2017-01-30T13:54:46Z","abstract_excerpt":"Based on Stokes' theorem we derive a non-holomorphic functional calculus for matrices, assuming sufficient smoothness near eigenvalues, corresponding to the size of related Jordan blocks. It is then applied to the complex conjugation function $\\tau: z \\mapsto \\overline z$. The resulting matrix agrees with the hermitian transpose if and only if the matrix is normal. Two other, as such elementary, approaches to define the complex conjugate of a matrix yield the same result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08597","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"}