eigenvalue

问题 This is matrix B B = [1 2 0 ; 2 4 6 ; 0 6 5] The result of eig(B) is: {-2.2240, 1.5109, 10.7131} and the characteristic polynomial of B by this link is syms x polyB = charpoly(B,x) x^3 - 10*x^2 - 11*x + 36 but the answer of solve(polyB) is 133/(9*(3^(1/2)*5492^(1/2)*(i/3) + 1009/27)^(1/3)) + ((3^(1/2)*5492^(1/2)*i)/3 + 1009/27)^(1/3) + 10/3 (3^(1/2)*(133/(9*(3^(1/2)*5492^(1/2)*(i/3) + 1009/27)^(1/3)) - ((3^(1/2)*5492^(1/2)*i)/3 + 1009/27)^(1/3))*i)/2 - 133/(18*(3^(1/2)*5492^(1/2)*(i/3) + 1009

问题 I am trying to generate points within ellipsoid and then trying to fit with smooth ellipsoid surfaces. The goal is to fit with unknown data where i have to find value of a,b and c in 3 principal axes. Rinv should be equivalent to pc. But what i am getting pc in different order. So i have to find correct order to rotate my data to matlab coordinate. a=3; b=5; c=1; index=1; for i=1:500000 x=10*rand-5; y=10*rand-5; z=10*rand-5; if ((x^2/a^2) + (y^2/b^2) + (z^2/c^2) -1) <0 C(index,:)=[x,y,z];

问题 I am using LAPACK's ssteqr function to calculate eigenvalues/eigenvectors. The documentation for ssteqr says that the eigenvalues are sorted "in ascending order" . Is it reasonable to assume that the list of eigenvectors is also sorted in ascending order? 回答1: Yes, it is reasonable to assume that the eigenvectors are ordered so that the i -th eigenvector corresponds to the i -th eigenvalue. Nevertheless, if I were you, I would check for each eigenvalue the result of the multiplication of the

问题 I am grad student trying to rewrite my MATLAB prototype code into C++ code using Eigen and LAPACK. Generalised eigenvalue solver (A*x=lamba*B*x) takes some part in this program. Because Eigen's generalised eigen solver could result in wrong eigenvalue (in my experience), I decided to go with LAPACK (using Accelerate framework in OS X) The code below is the C++ translation of tgevc example http://www.nag.com/numeric/fl/manual/pdf/F08/f08ykf.pdf that I wrote. Everything looks fine unless I

问题 I'm trying to compute eigenvalues of a symbolic complex matrix M of size 3x3 . In some cases, eigenvals() works perfectly. For example, the following code: import sympy as sp kx = sp.symbols('kx') x = 0. M = sp.Matrix([[0., 0., 0.], [0., 0., 0.], [0., 0., 0.]]) M[0, 0] = 1. M[0, 1] = 2./3. M[0, 2] = 2./3. M[1, 0] = sp.exp(1j*kx) * 1./6. + x M[1, 1] = sp.exp(1j*kx) * 2./3. M[1, 2] = sp.exp(1j*kx) * -1./3. M[2, 0] = sp.exp(-1j*kx) * 1./6. M[2, 1] = sp.exp(-1j*kx) * -1./3. M[2, 2] = sp.exp(-1j

问题 Here's my code: def topK(dataMat,sensitivity): meanVals = np.mean(dataMat, axis=0) meanRemoved = dataMat - meanVals covMat = np.cov(meanRemoved, rowvar=0) eigVals,eigVects = np.linalg.eig(np.mat(covMat)) I get the error in the title on the last line above. I suspect has something to do with the datatype, so, here's an image of the variable and datatype from the Variable Explorer in Spyder: I've tried changing np.linalg.eig(np.mat(covMat)) to np.linalg.eig(np.array(np.mat(covMat))) and to np

问题 I am having some issues with scipy's eigh function returning negative eigenvalues for positive semidefinite matrices. Below is a MWE. The hess_R function returns a positive semidefinite matrix (it is the sum of a rank one matrix and a diagonal matrix, both with nonnegative entries). import numpy as np from scipy import linalg as LA def hess_R(x): d = len(x) H = np.ones(d*d).reshape(d,d) / (1 - np.sum(x))**2 H = H + np.diag(1 / (x**2)) return H.astype(np.float64) x = np.array([ 9.98510710e-02

问题 I've been doing some Geometrical Data Analysis (GDA) such as Principal Component Analysis (PCA). I'm looking to plot a Correlation Circle... these look a bit like this: Basically, it allows to measure to which extend the Eigenvalue / Eigenvector of a variable is correlated to the principal components (dimensions) of a dataset. Anyone knows if there is a python package that plots such data visualization? 回答1: I agree it's a pity not to have it in some mainstream package such as sklearn. Here

问题 what is the fastest method to calculate this, i saw some people using matrices and when i searched on the internet, they talked about eigen values and eigen vectors (no idea about this stuff)...there was a question which reduced to a recursive equation f(n) = (2*f(n-1)) + 2 , and f(1) = 1, n could be upto 10^9.... i already tried using DP, storing upto 1000000 values and using the common fast exponentiation method, it all timed out im generally weak in these modulo questions, which require

问题 #eigen values and vectors a <- matrix(c(2, -1, -1, 2), 2) eigen(a) I am trying to find eigenvalues and eigenvectors in R. Function eigen works for eigenvalues but there are errors in eigenvectors values. Is there any way to fix that? 回答1: Some paper work tells you the eigenvector for eigenvalue 3 is (-s, s) for any non-zero real value s ; the eigenvector for eigenvalue 1 is (t, t) for any non-zero real value t . Scaling eigenvectors to unit-length gives s = ± sqrt(0.5) = ±0.7071068 t = ± sqrt