# Questions tagged [generalized-eigenvector]

This tag is for questions relating to Generalized-eigenvector, a vector which satisfies certain criteria which are more relaxed than those for an (ordinary) eigenvector.

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### Question involving eigenspaces and generalized eigenspaces

I need to solve the question given above; however, I am unsure of how to proceed exactly; am I required to use the invertibility of $U$ to somehow show the two equalities? Any help would be ...
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### How to determine the Basis transformation with first finding eigenvector?

How to determine the Basis transformation and all the explicit lambdas with the matrix (let say $A$) below? \begin{pmatrix}1&a&0\\ a&1&0\\ 0&0&b\end{pmatrix} I know that we ...
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### Generalized Eigenvalue Problem - How to solve? Fisherfaces

I'm trying to do picture recognition. There are 3 types of methods from OpenCV library. Eigenfaces, Fisherfaces and Local Binary Pattern Histogram. These are good, but in practice, Fisherfaces is the ...
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### Eigenvalue-like problem for block matrices — numerical solutions

Consider the following matrix equation  \left[\begin{array}{cc}{A_{11}} & {A_{12}} \\ {A_{21}} & {A_{22}}\end{array}\right]\left[\begin{array}{c}{v_1} \\ {v_2} \end{array}\right] = \left[\...
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### How to get “true” (orthonormal) eigenvectors when I got generalized eigenvectors by solution Hv=eSv

I solved equation $H[v] = eS[v]$ using some numerical package (e,V = scipy.lingalg.eig(H,S)) There $[v]$ is matrix of all generalized eigenvectors $v_i$, $H$ is ...
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### Spectral theory; separation of spectrum, eigenprojections

I have been reading Kato's perturbation theory book and on spectral theory in general, and I have a question regarding the separation of spectrum (c.f. Kato, Perturbation theory for linear operators, ...
### Power iteration for generalized eigenvalue problem $Ax = \lambda B x$ where $A$ and $B$ are singular
Generalized eigenvalue problem can be reduced to eigenvalue problem $B^{-1} A x = \lambda x$ if $B$ is non-singular matrix. Then, the standard power iteration method can be applied. How can I use the ...