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Results tagged with perturbation
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user 13650
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The Eigenvalue Problem: Perturbation Theory
Counterexample: $$K = \pmatrix{0 & 1\cr 0 & 0\cr},\ \rho(K) = 0,\ {\bf u} = (0,1),\ {\bf v} = \pmatrix{1\cr 0\cr},\
A = \pmatrix{1 & 0\cr 0 & 1\cr}$$
Normalize however you want, $({\bf u}, A {\bf v} …
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Is Rellich's function valued theorem valid for a rank defficient function valued matrix?
Yes, Rellich's theorem does not require the eigenvalues to be distinct. See e.g. Reed and Simon, "Methods of modern mathematical physics vol. 4: Analysis of Operators", Chapter XII (in particular Pro …
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