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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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Sorting eigenvectors by their eigenvalues (associated sorting)

I have an unsorted vector of eigenvalues and a related matrix of eigenvectors. I'd like to sort the columns of the matrix with respect to the sorted set of eigenvalues. (e.g., if eigenvalue[3] moves to eigenvalue[2], I want column 3 of the…
fbrereto
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numpy scipy -- keep eigenvalues in stringent order

I compute the eigenvalues of a time-dependent matrix using scipy.linalg.eigvalsh(matrix) for each point in time. Then I collect them in a nested list ([[result for time 1], [result for time 2], etc.] and store the list via numpy.savetxt. My problem…
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Largest eigenvalues (and corresponding eigenvectors) in C++

What is the easiest and fastest way (with some library, of course) to compute k largest eigenvalues and eigenvectors for a large dense matrix in C++? I'm looking for an equivalent of MATLAB's eigs function; I've looked through Armadillo and Eigen…
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least eigenvalue in python

I was wondering if numpy has efficient implementation to compute the largest or smallest eigenvalue of symmetric matrix, without the full spectral decomposition if possible. I find the following modules implement the…
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how to find Eigenvalues for non quadratic matrix

I want to make similar graphs to this given on the picture: I am using Fisher Iris data and employ PCA to reduce dimensionality. this is code: load fisheriris [pc,score,latent,tsquare,explained,mu] = princomp(meas); I guess the eigenvalues are…
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Routh-Hurwitz useful when I can just calculate eigenvalues?

This is for self-study of N-dimensional system of linear homogeneous ordinary differential equations of the form: dx/dt=Ax where A is the coefficient matrix of the system. I have learned that you can check for stability by determining if the real…
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Is it worth using IPython parallel with scipy's eig?

I'm writing a code which has to compute large numbers of eigenvalue problems (typical matrices dimension is a few hundreds). I was wondering whether it is possible to speed up the process by using IPython.parallel module. As a former MATLAB user and…
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Computing Eigen Values and Eigen Vector using IronPython2.7

This might be a frequent problem for IronPython users. But I am new to python. I wish to compute Eigen Value and Eigen vector of around 50x50 matrix using IronPython2.7 I explored possibilities of using Numpy and Scipy, but they are not supported…
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How to figure out eigenvalues of a matrix in matlab when all entries of matrix are variables?

I have a matrix with a bunch of unknown constants such as the one below: a*b -c -d 0 -c e -a -b-d -d -a d -e 0 -b-d -e a As you may realize it is symmetric about the diagonal and therefore,…
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Estimating the variance of eigenvalues of sample covariance matrices in Matlab

I am trying to investigate the statistical variance of the eigenvalues of sample covariance matrices using Matlab. To clarify, each sample covariance matrix is constructed from a finite number of vector snapshots (afflicted with random white…
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Find a matrix that gives same result when multiplied by a constant or another matrix

I have got a problem like A*x=lambda*x, where A is of order d*d, x is of order d*c and lambda is a constant. A and lambda are known and the matrix x is unknown. Is there any way to solve this problem in matlab?? (Like eigen values but x is a d*c…
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How can I perform face recognition using an eigenfaces value in OpenCV?

After using OpenCV's PCACompute function as shown below, I have a Mat representing mean and a Mat of eigenvectors. org.opencv.core.Core.PCACompute(datiOriginali,mean, eigenvectors,0); datiOriginali is my input Mat, mean is the mean value Mat and…
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R basic function eigen has problem with symmetric matrices

eigen is a base R function that returns eigenvectors and eigenvalues for a given matrix. I just found that it can be not robust for the symmetric matrices when you specify this explicitly using symmetric=TRUE. I show the issue below. Are there…
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Julia: all eigenvalues of large sparse matrix

I have a large sparse matrix, for example, 128000×128000 SparseMatrixCSC{Complex{Float64},Int64} with 1376000 stored entries. How to quickly get all eigenvalues of the sparse matrix ? Is it possible ? I tried eigs for 128000×128000 with 1376000…
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Sort 3D eigenvector array using eigenvalues

I am trying to re-order a tensor of eigenvalues and eigenvectors in numpy in descending order. I have partially used this answer to do so. I am now trying to do the ordering on an array of eigenvalues of shape (32448,3) and eigenvectors of shape…
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