Bauer–Fike Theorem

(Theory)

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What is Bauer–Fike theorem?

In mathematics, the Bauer–Fike theorem is a standard result in the perturbation theory of the eigenvalue of a complex-valued diagonalizable matrix. In its substance, it states an absolute upper bound for the deviation of one perturbed matrix eigenvalue from a properly chosen eigenvalue of the exact matrix. Informally speaking, what it says is that the sensitivity of the eigenvalues is estimated by the condition number of the matrix of eigenvectors. The theorem was proved by Friedrich L. Bauer and C. T. Fike in 1960.

Technology Types

mathematical theorempropositionspectral theorystatementtheoremtheorems in analysistheory

Synonyms

Bauer-Fike Theorem

Translations

Satz von Bauer-Fike (de)

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