Bauer-Fike theorem

Let λ~ be a complex numberMathworldPlanetmathPlanetmath and u~ be a vector with u~p=1, and let r=Au~-λ~u~ (usually, λ~ and u~ are considered to be approximation of an eigenvalueMathworldPlanetmathPlanetmathPlanetmathPlanetmath and of an eigenvectorMathworldPlanetmathPlanetmathPlanetmath of A). Assume A is diagonalizablePlanetmathPlanetmath and A=XDX-1, with D a diagonal matrixMathworldPlanetmath. Then the matrix A has an eigenvalue λ which satisfies the inequality:


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Title Bauer-Fike theorem
Canonical name BauerFikeTheorem
Date of creation 2013-03-22 14:48:31
Last modified on 2013-03-22 14:48:31
Owner Andrea Ambrosio (7332)
Last modified by Andrea Ambrosio (7332)
Numerical id 12
Author Andrea Ambrosio (7332)
Entry type Theorem
Classification msc 15A42