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On the eigenvalues of the matrix pencilA+μB

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Summary

The number of independent invariants ofn×n matricesA, B and their products on which the eigenvalues λ(μ) of the matrix pencilA+μB depend is determined by means of the theory of algebraic invariants and combinatorial analysis. Formulas are displayed for coefficients for the calculation of λ(μ) forn≤5.

Zusammenfassung

Wir bestimmen die Anzahl der unabhängigen Invarianten dern×n MatrizenA, B und ihrer Produkte, von denen die Eigenwerte λ(μ) der MatrixbüschelA+μB abhängen, mittels der Theorie der algebraischen Invarianten und mittels kombinatorischer Analyse. Formeln für Koeffizienten zur Berechnung von λ(μ) werden angegeben fürn≤5.

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Author notes

  1. H. G. Othmer

    Present address: Department of Mathematics, Rutgers University, 08903, New Brunswick, N.J., USA

Authors and Affiliations

  1. Dept. of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota, USA

    H. G. Othmer & L. E. Scriven

Authors
  1. H. G. Othmer
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  2. L. E. Scriven
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Othmer, H.G., Scriven, L.E. On the eigenvalues of the matrix pencilA+μB . Journal of Applied Mathematics and Physics (ZAMP) 24, 135–139 (1973). https://doi.org/10.1007/BF01594006

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  • DOI: https://doi.org/10.1007/BF01594006

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