eigenvector

my problem is the following: using scipy.linalg.eig to get eigenvectors and eigenvalues i see that all my eigenvalues have multiplicity 1 yet when i run the code below it doesn't confirm that the eigenvectors are orthogonal as they should be in this case. any reason why this would be? or how to fix it? import scipy as SP import numpy as NP from scipy import linalg from numpy import linspace,asscalar,argsort import cmath import time matA=SP.array([[-0.0001, 0., 0., 0.00001, 0., 0., 0.00002, 0.],[0., -0.0002, 0., 0., 0., 0., 0., 0.],[0., 0., -0.00015, 0., 0., -9.*10**-6, 0., -0.00005],[0.00001,

I have a matrix A A = [ 124.6,95.3,42.7 ; 95.3,55.33,2.74 ; 42.7,2.74,33.33 ] The eigenvalues and vectors: [V,D] = eig(A) How do I show the eigenvalues are mutually perpendicular? I've tried that if the dot product of the eigenvalues are zero, this demonstrates they are mutually perpendicular, but how would you compute this in MATLAB? I tried the following code transpose(diag(D)) * diag(D) %gives 4.1523e+04 Also, how can I verify the definition of eigenvalues and vector holds: A e_i - L_i e_i = 0 The above equation: for i equal 1 to 3. For a real, symmetric matrix all eigenvales are positive

Could you please explain why there is a sign difference in some of the eigenvectors (2-4)? Does this difference affect further calculation in further calculations, e.g dimensionality reduction? Matlab: N = 5000; dataA = rand(N,5); covA = cov(dataA); %covA = dataA*dataA'/(length(dataA)-1); covA = covA + eps.*eye(size(covA)); [~,pA] = chol(covA); assert(pA==0,'A is not possitive definite') dataB = rand(N,5); covB = cov(dataB); %covB = dataB*dataB'/(length(dataB)-1); covB = covB + eps.*eye(size(covB)); [~,pB] = chol(covB); assert(pB==0,'B is not possitive definite') [V,D] = eig(covA, covB); V =

I am calculating eigenvectors in Matlab and Numpy, but getting different results. I was under the impression there was only one set of eigenvectors for a given matrix, however both of these outputs seem valid. Here is my matlab code: m = [ 1.4675 + 0.0000i 0.1669 + 1.2654i; 0.1669 - 1.2654i 1.3085 + 0.0000i] [eig_vec,eig_val] = eig(m) eig_val contains: eig_val = 0.1092 0 0 2.6668 eig_vec contains: eig_vec = 0.0896 + 0.6789i 0.0953 + 0.7225i -0.7288 + 0.0000i 0.6848 + 0.0000i Here is my python code: m = np.array([[1.46753694+0.j, 0.16692111+1.26535838j], [0.16692111-1.26535838j, 1.30851770+0.j]

I try to use eig_pair to get Eigen decomposition for pair of general dense square matrices A and B of the same size, such that A*eigvec = B*eigvec*diagmat(eigval), but the result doesn't match the Matlab function eig. for example: A= [1,2;3,4] B=[2,4;5,8] in Matlab: [u,v] = eig(A,B) result: u = -1.0000 -0.0000 0.5000 -1.0000 v = 1.0000 0 0 0.5000 in armadillo: eig_pair(v,u,A,B) result: u: 9.9301e-016 -1.0000e+000 1.0000e+000 5.0000e-001 v: 0.5000 1.0000 My question is: how to get the values of u and v that match the results in Matlab? Looking forwards to your reply!!! Eigenvectors are not