Trace and Determinant

  • Israel Gohberg
  • Seymour Goldberg
  • Marinus A. Kaashoek
Part of the Operator Theory: Advances and Applications book series (OT, volume 49)


The first section of this chapter has an introductory character; it explains the principles we use to define the trace and determinant. The precise definitions are given in the next two sections where we also derive the first properties of the trace and determinant. In Section 4 the analyticity of det(IλA) as a function of λ is proved. The main theorem is given in the sixth section and expresses trace and determinant in terms of the eigenvalues. Some technical results from complex function theory, which are used in the proof of the main theorem, are derived in Section 5. The connections with the classical Fredholm determinant are described in Section 7. The last section contains as a first application two completeness theorems for eigenvectors and generalized eigenvectors.


Integral Operator Entire Function Trace Class Finite Rank Algebraic Multiplicity 
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Copyright information

© Springer Basel AG 1990

Authors and Affiliations

  • Israel Gohberg
    • 1
  • Seymour Goldberg
    • 2
  • Marinus A. Kaashoek
    • 3
  1. 1.School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact SciencesTel-Aviv UniversityTel-AvivIsrael
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA
  3. 3.Faculteit Wiskunde en InformaticaVrije UniversiteitAmsterdamThe Netherlands

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