Functional Calculus and Derivation

  • Fumio HiaiEmail author
  • Dénes Petz
Part of the Universitext book series (UTX)


Let \(A\in \mathbb {M}_n({\mathbb C})\) and \(p(x):=\sum _i c_i x^i\) be a polynomial. It is quite obvious that by \(p(A)\) we mean the matrix \(\sum _i c_i A^i\). So the functional calculus is trivial for polynomials.

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Authors and Affiliations

  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  2. 2.Alfréd Rényi Institute of MathematicsBudapestHungary
  3. 3.Department for Mathematical AnalysisBudapest University of Technology and EconomicsBudapestHungary

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