eigenvector

I have noticed there is a difference between how matlab calculates the eigenvalue and eigenvector of a matrix, where matlab returns the real valued while numpy's return the complex valued eigen valus and vector. For example: for matrix: A= 1 -3 3 3 -5 3 6 -6 4 Numpy: w, v = np.linalg.eig(A) w array([ 4. +0.00000000e+00j, -2. +1.10465796e-15j, -2. -1.10465796e-15j]) v array([[-0.40824829+0.j , 0.24400118-0.40702229j, 0.24400118+0.40702229j], [-0.40824829+0.j , -0.41621909-0.40702229j, -0.41621909+0.40702229j], [-0.81649658+0.j , -0.66022027+0.j , -0.66022027-0.j ]]) Matlab: [E, D] = eig(A) E -0

I create an arbitrary 2x2 matrix: In [87]: mymat = np.matrix([[2,4],[5,3]]) In [88]: mymat Out[88]: matrix([[2, 4], [5, 3]]) I attempt to calculate eigenvectors using numpy.linalg.eig: In [91]: np.linalg.eig(mymat) Out[91]: (array([-2., 7.]), matrix([[-0.70710678, -0.62469505], [ 0.70710678, -0.78086881]])) In [92]: eigvec = np.linalg.eig(mymat)[1][0].T In [93]: eigvec Out[93]: matrix([[-0.70710678], [-0.62469505]]) I multiply one of my eigenvectors with my matrix expecting the result to be a vector that is a scalar multiple of my eigenvector. In [94]: mymat * eigvec Out[94]: matrix([[-3

I've searched a lot for this but I can't find any answer about how the two methods 'eig' and 'eigs' differ. What is the difference between the eigenvalues and eigenvectors received from them? They use different algorithms, tailored to different problems and different goals. eig is a good, fast, general use eigenvalue/vector solver. It is appropriate for use when your matrix is of a realistic size that fits well in memory, and when you need all of the eigenvalues/vectors. Sparse matrices do not work at all in eig . Eigs is a solver that is more appropriate for when you need only a limited

I am trying to find the eigenvalues/vectors for the following matrix: A = np.array([[1, 0, 0], [0, 1, 0], [1, 1, 0]]) using the code: from numpy import linalg as LA e_vals, e_vecs = LA.eig(A) I'm getting this as the answer: print(e_vals) [ 0. 1. 1.] print(e_vecs) [[ 0. 0.70710678 0. ] [ 0. 0. 0.70710678] [ 1. 0.70710678 0.70710678]] However, I believe the following should be the answer. [1] Real Eigenvalue = 0.00000 [1] Real Eigenvector: 0.00000 0.00000 1.00000 [2] Real Eigenvalue = 1.00000 [2] Real Eigenvector: 1.00000 0.00000 1.00000 [3] Real Eigenvalue = 1.00000 [3] Real Eigenvector: 0

I'm trying to fit a 2D Gaussian to an image. Noise is very low, so my attempt was to rotate the image such that the two principal axes do not co-vary, figure out the maximum and just compute the standard deviation in both dimensions. Weapon of choice is python. However I got stuck at finding the eigenvectors of the image - numpy.linalg.py assumes discrete data points. I thought about taking this image to be a probability distribution, sampling a few thousand points and then computing the eigenvectors from that distribution, but I'm sure there must be a way of finding the eigenvectors (ie.,

In MATLAB, when I run the command [V,D] = eig(a) for a symmetric matrix, the largest eigenvalue (and its associated vector) is located in last column. However, when I run it with a non-symmetric matrix, the largest eigenvalue is in the first column. I am trying to calculate eigenvector centrality which requires that I take the compute the eigenvector associated with the largest eigenvalue. So the fact that the largest eigenvalue appears in two separate places it makes it difficult for me to find the solution. gnovice You just have to find the index of the largest eigenvalue in D , which can