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Questions tagged [eigenvalue]

The eigenvalue is the factor by which the eigenvector is scaled when multiplied by the matrix.

The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the matrix, remain parallel to the original vector. For each eigenvector, the corresponding eigenvalue is the factor by which the eigenvector is scaled when multiplied by the matrix. The prefix eigen- is adopted from the German word "eigen" for "own"[1] in the sense of a characteristic description. The eigenvectors are sometimes also called characteristic vectors. Similarly, the eigenvalues are also known as characteristic values.

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geom_bar of named number vector

I'm trying to do a simple thing that's very easy in base R plot, but for versatility reasons, I want to use ggplot instead and I can't find the best way to do so. I have a named number vector of PCA eigenavalues: nums <- c(2.491301e-01,…
Jake L
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Sparse and Complex Generalized Eigenvalue Problem

I have been trying to solve a complex and sparse generalized eigenvalue problem. As far as I see in the documentation, it should be possible to do with Eigen. So I wanted to perform this with a test case with A and B matrices are 2 by 2 but still…
Arjo
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Numpy .eig returns matrices row permuted

I'm implementing an SVD algorithm and wanting to use the .eig method (following this tutorial here: https://datajobs.com/data-science-repo/SVD-Tutorial-[Kirk-Baker].pdf) We are given a 2x3 matrix: A = [[3,1,1],[-1,3,1]] And the first step is to work…
Nihir
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Hessian of Gaussian eigenvalues on 3D images with Python

I have a 3D image and I want to calculate the Hessian of Gaussian eigenvalues for this image. I would like to have the three eigenvalues of the Hessian approximation for each voxel. This feature seems to be something very common in image…
Titouan
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Hessian of Gaussian eigenvalues for 3D image with Python

I have a 3D image and I want to calculate the Hessian of Gaussian eigenvalues for this image. I would like to have the three eigenvalues of the Hessian approximation for each voxel. This feature seems to be something very common in image…
Titouan
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Eigenvalues of sample covariance far from eigenvalues of covariance

I wrote the following code to create a random matrix Sigma with specified eigenvalues, and then sample vectors from multivariate normal distribution with zero mean and covariance Sigma. def generate_data(N, d): eigenvalues = [0] * (d + 1) …
Oria Gruber
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fast computation of matrix trace norm in R

I have a square symmetric real matrix S of dimension 31. I want to compute its trace (nuclear) norm, Frobenius (Hilbert--Schmidt) norm and operator (spectral) norm. I am using eigen: x <- eigen(S, only.values =…
YZS
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How to deal with non-zero (actually zero) eigen value in R?

Using R, I'm trying to verify SVD with simple 3-by-2 matrix M by calculating eigenvalues and vectors of transposed matrix, say N1 and N2 shown below. column1 <- c(1,2,3) column2 <- c(4,5,6) M <- cbind(column1,column2) N1 <- M %*% t(M) N2 <- t(M) %*%…
hiro7
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How do I improve the accuracy of calculating Eigenvalues using GNU GSL

I am trying to switch from Mathematica to C on a windows platform. My most difficult task is calculating Eigenvalues and Eigenvectors for real non-symmetric matrices up to about 50x50. I have succeeded in getting Microsoft Visual Studio to run the…
Jim C
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Cannot perform generalized eigenvalue problem with positive definitive symmetrical matricies with OjAlgo - What wrong am I doing?

Trying to solve generalized eigenvalues on the form: A*V = B*V*D By using OjAlgo. According to the documentation here A and B bust be real symmetric or complex Hermitian and B is positive definite. In this case, both A and B are symmetrical and…
euraad
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What is the equivalent code for [V, D] = eig(A, B) in Python? Generalized Eigenvalue Problem

I'm trying to solve Generalized Eigenvalue Problem with Java and I'm currently using OjAlgo, but it cannot solve random symmetrical A and B. Only positive definite symmetrical A and B for the moment. My A and B are random symmetrical. Not positive…
euraad
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Eigenvalues & Eigenvectors out of non-numbers matrix

I wanted to know if there is a way of getting the eigenvalues and eigenvector of a matrix A, when its not made out of numbers, in Python. For example: [[a,b] [c,d]] I tried to make a program so that I could input any matrix to a website called…
Lucio Coro
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Linear Algebra in R

I wanted to know if there is a specific function that allows you to get the basis of the eigenspace, or the eigenvector with respect to each eigenvalue.
Anapaulacg
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Different results with PCA and SVD on data with same units

At the beginning, i had 400,000 images that were normalized (gray value increase). After that i did a DFT of each picture and got data of 400000 samples with 3200 absolute fourier-coefficients. Now I would like to do a PCA and SVD. Since my data is…
Len01
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How to determine eigenvalues for a matrix with one symbolic variable?

I am trying to find the eigenvalues of a matrix in which all the elements contain a symbolic variable 'w' in MATLAB. When using the eig function with a small matrix, for example 5x5, Matlab returns the answer in short time but for my case with 75x75…
Kartik Kanugo
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