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The verification of multiplicity support of a defective eigenvalue of a real matrix

Author

Listed:
  • Li, Zhe
  • Zhang, Chunlei

Abstract

Computing a defective eigenvalue is an ill-posed problem if components of the matrix are approximate data. Using the definition of multiplicity support of a defective eigenvalue introduced by Zeng, we consider the verification about the sensitivity and computation of a defective eigenvalue of a real matrix. We discuss how to construct a slightly perturbed interval matrix which is guaranteed to possess a real matrix with computed defective eigenvalue of computed multiplicity support. Furthermore, we also obtain an interval matrix which is guaranteed to possess a real matrix. The columns of the real matrix span the corresponding eigenvector space.

Suggested Citation

  • Li, Zhe & Zhang, Chunlei, 2022. "The verification of multiplicity support of a defective eigenvalue of a real matrix," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    • Handle: RePEc:eee:apmaco:v:414:y:2022:i:c:s0096300321007554
    DOI: 10.1016/j.amc.2021.126671
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