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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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Solving Eigen System in c#?

Do you know of a good library/way that I can use to solve an eigen system in c#? My data is 2D/3D and I want to get direction and length of first and second eigen vectors to evaluate how my data is elongated in 2D space. Thanks
Mo Valipour
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Solving Generalized eigenvectors and eigen values to get a common basis

I am looking for solving a generalized eigenvectors and eigen value problem in Matlab. For this, I have tested 2 methods. if Generalized problem is formulated as : Then, we could multiply by B^(-1) on each side, such as : So, from a theorical…
user1773603
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Why does the product of the eigenvector and the corresponding eigenvalue not equal the product of the original matrix and the eigenvector?

When I multiply an eigenvector by a matrix, it should result in the same output as multiplying that eigenvector by its corresponding eigenvalue. I am trying to verify that my eigenvectors and eigenvalues are working as advertised, but the outputs…
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any fuction in python as polyeig() in matlab?

i'm trying to solve a polynomial eigen value problem in python and i need a function like polyeig in matlab, is there any library that is capable of doing this? The problem that i'm trying to solve is of the…
jsp
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Confused about Eigen QR decomposition

I am confused about Eigen's QR decomposition. My understanding is that the matrix Q is stored implicitly as a sequence of Householder transformations, and that the matrix R is stored as an upper triangular matrix, and that the diagonal of R contains…
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Can we calculate only the n-th eigenvalue and eigenvector of a very large sparse matrix?

I have a very big sparse matrix A = 7Mi-by-7Mi matrix. I am using Matlab's eigs(A,k) function which can calculate first k eigenvalues and vectors. I need all of its eigenvector and values. But I can't store all of the eigenvectors because it…
Luqman Saleem
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Finding Largest Eigenvalue of Huge Sparse Matrix

I am trying to find the largest eigenvalue of an incredibly sparse adjacency matrix. I have tried using all the approaches I see available: mat = scipy.io.mmread(f) mat = scipy.sparse.csr_matrix(mat) G = nx.to_networkx_graph(mat) mat = None #…
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Eigendecomposition makes me wonder in numpy

I test the theorem that A = Q * Lambda * Q_inverse where Q the Matrix with the Eigenvectors and Lambda the Diagonal matrix having the Eigenvalues in the Diagonal. My code is the following: import numpy as np from numpy import linalg as…
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Find zeros of the characteristic polynomial of a matrix with Python

Given an N x N symmetric matrix C and an N x N diagonal matrix I, find the solutions of the equation det(λI-C)=0. In other words, the (generalized) eigenvalues of C are to be found. I know few ways how to solve this in MATLAB using build-in…
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Modelica linear analysis

I am new into Modelica/Dymola-modeling. I started to model fluid models for my master-thesis (pipes, heaters, control). My professor suggested: Check the eigenvalues of the systems and the ratio of them (and if the systems is stiff). So did the…
Matias
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Find the eigenvalues of a subset of Dataframe in Python

I have a matrix in the form of DataFrame df= 6M 1Y 2Y 4Y 5Y 10Y 30Y 6M n/a n/a n/a n/a n/a n/a n/a 1Y n/a 1 0.9465095 …
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Matlab Not Returning Orthonormal Matrix of Eigenvectors

When I try to find the eigen-decomposition of a matrix in Matlab that has a repeated eigenvalue but is NOT defective, it is not returning an orthonormal matrix of eignevectors. For example: k = 5; repeats = 1; % First generate a random matrix of…
rwolst
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Java package for eigenvector/eigenvalues computation?

which java package do you recommend for computing eigenvectors/eigenvalues? I know about JMathTools and JAMA; do you have some pro/cons for these packages? Other suggestions?
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How does numpy.linalg.eig decide on order in which eigenvalues are returned?

When I use numpy.linalg.eig like eValues, eVectors = numpy.linalg.eig(someMatrix) the eValues returned are almost in descending order. How does numpy.linalg.eig decide on order in which eigenvalues are returned?
user3731622
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Tool to diagonalize large matrices

I want to compute a diffusion kernel, which involves taking exp(b*A) where A is a large matrix. In order to play with values of b, I'd like to diagonalize A (so that exp(A) runs quickly). My matrix is about 25k x 25k, but is very sparse - only…
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