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Results tagged with eigenvector
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user 13093
0
votes
1
answer
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Stability of eigenvectors for diagonal perturbations
In a previous question I asked about the stability of eigenvalues with respect to diagonal perturbations. Following results from the book Matrix Analysis (by Roger A. Horn & Charles R. Johnson) the r …
- 2,222
7
votes
1
answer
6k
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Eigenvectors as continuous functions of matrix - diagonal perturbations
Does the first eigenvalue and the first eigenvector of $A+D$ vary continuously for $\|D\|_1 <\varepsilon$ ($\varepsilon$ can be as small as possible, and $\|\cdot \|_1$ is the $L^1$ norm)? … In the case this is true, it is possible to bound the variation of the eigenvector in terms of $\|D\|_1$? …
- 2,222