eigenvector

eigenvalues, eigenvectors = linalg.eig(K) How can I print just eigenvectors of len(K) . So if there is K , 2x2 matrix, I get 4 eigenvectors, how can I print just 2 of them if there is len(K)=2 .... Many thanks You are getting two vectors of length two, not four vectors. For example: In [1]: import numpy as np In [2]: K=np.random.normal(size=(2,2)) In [3]: eigenvalues, eigenvectors = np.linalg.eig(K) In [4]: eigenvectors Out[4]: array([[ 0.83022467+0.j , 0.83022467+0.j ], [ 0.09133956+0.54989461j, 0.09133956-0.54989461j]]) In [5]: eigenvectors.shape Out[5]: (2, 2) The first vector is

I have a matrix such as this example (my actual matrices can be much larger) A = [-1 -2 -0.5; 0 0.5 0; 0 0 -1]; that has only two linearly-independent eigenvalues (the eigenvalue -1 is repeated). I would like to obtain a complete basis with generalized eigenvectors . One way I know how to do this is with Matlab's jordan function in the Symbolic Math toolbox, but I'd prefer something designed for numeric inputs (indeed, with two outputs, jordan fails for large matrices: "Error in MuPAD command: Similarity matrix too large."). I don't need the Jordan canonical form, which is notoriously unstable

While using princomp() function in R, the following error is encountered : "covariance matrix is not non-negative definite" . I think, this is due to some values being zero (actually close to zero, but becomes zero during rounding) in the covariance matrix. Is there a work around to proceed with PCA when covariance matrix contains zeros ? [FYI : obtaining the covariance matrix is an intermediate step within the princomp() call. Data file to reproduce this error can be downloaded from here - http://tinyurl.com/6rtxrc3] The first strategy might be to decrease the tolerance argument. Looks to me

Short version of my question : What would be the optimal way of calculating an eigenvector for a matrix A , if we already know the eigenvalue belonging to the eigenvector? Longer explanation : I have a large stochastic matrix A which, because it is stochastic, has a non-negative left eigenvector x (such that A^Tx=x ). I'm looking for quick and efficient methods of numerically calculating this vector. (Preferrably in MATLAB or numpy/scipy - since both of these wrap around ARPACK/LAPACK, any one would be fine). I know that 1 is the largest eigenvalue of A , so I know that calling something like

I am using princomp in R to perform PCA. My data matrix is huge (10K x 10K with each value up to 4 decimal points). It takes ~3.5 hours and ~6.5 GB of Physical memory on a Xeon 2.27 GHz processor. Since I only want the first two components, is there a faster way to do this? Update : In addition to speed, Is there a memory efficient way to do this ? It takes ~2 hours and ~6.3 GB of physical memory for calculating first two components using svd(,2,) . Dirk Eddelbuettel You sometimes gets access to so-called 'economical' decompositions which allow you to cap the number of eigenvalues /