search for: eigenvalues

Dear all, I want to compute the eigenvalues of a complex matrix for some statistics. Comparing it to its matlab/octave sibling, I don't get the same eigenvalues in R computing it from the exact same matrix. In R, I used eigen() and arpack() that give different eigenvalues. In matlab/octave I used eig() and eigs() that give out the same...

...lambda such that 0 < \lambda < 1, I would like to generate an N by N stochastic matrix (a matrix with all the rows summing to 1), such that it has the second largest eigenvalue equal to \lambda (Note: the dominant eigenvalue of a stochastic matrix is 1). I don't care what the other eigenvalues are. The second eigenvalue is important in that it governs the rate at which the random process given by the stochastic matrix converges to its stationary distribution. Does anyone know of an algorithm to do this? Thanks for any help, Ravi. -----------------------------------------------...

I'm trying to test if a correlation matrix is positive semidefinite. My understanding is that a matrix is positive semidefinite if it is Hermitian and all its eigenvalues are positive. The values in my correlation matrix are real and the layout means that it is symmetric. This seems to satisfy the Hermitian criterion so I figure that my real challenge is to check if the eigenvalues are all positive. I've tried to use eigen(base) to determine the eigenvalues. T...

Dear All, I want to know if there is some easy and reliable way to estimate the number of dominant eigenvalues when applying PCA on sample covariance matrix. Assume x-axis is the number of eigenvalues (1, 2, ....,n), and y-axis is the corresponding eigenvalues (a1,a2,..., an) arranged in desceding order. So this x-y plot will be a decreasing curve. Someone mentioned using the elbow (knee) method to find t...

Dear all, I've used the 'prcomp' command to calculate the eigenvalues and eigenvectors of a matrix(gg). Using the command 'principal' from the 'psych' package  I've performed the same exercise. I got the same eigenvalues but different eigenvectors. Is there any reason for that difference? Below are the steps I've followed: 1. PRCOMP #d...

Hello, Can you get eigenvalues in addition to eigevectors using prcomp? If so how? I am unable to use princomp due to small sample sizes. Thank you in advance for your help! Rebecca Young -- Rebecca Young Graduate Student Ecology & Evolutionary Biology, Badyaev Lab University of Arizona 1041 E Lowell Tucson, AZ 85721-0088...

Hello, I am trying to construct two matrices, F and V, composed of partial derivatives and then find the eigenvalues of F*Inverse(V). I have the following equations in ryacas notation: > library(Ryacas) > FIh <- Expr("betah*Sh*Iv") > FIv <- Expr("betav*Sv*Ih") > VIh <- Expr("(muh + gamma)*Ih") > VIv <- Expr("muv*Iv") I successfully found...

I have been looking at the "eigen" function and have reintroduced the ability to compute (right) eigenvalues and vectors for non-symmetric matrices. I've also made "eigen" complex capable. The code is based on the eispack entry points RS, RG, CH, CG (which is what S appears to use too). The problem with both the S and R implementations is that they consume huge amounts of memory. Some of...

Dear R-users How can I get the eigenvalues out of an lda analysis? thanks a lot christoph -- Christoph Lehmann <christoph.lehmann at gmx.ch>

Dear all, I encounter some covariance matrix with quite small eigenvalues (around 1e-18), which are smaller than the machine precision. The dimension of my matrix is 17. Here I just fake some small matrix for illustration. a<-diag(c(rep(3,4),1e-18)) # a matrix with small eigenvalues b<-matrix(1:25,ncol=5) # define b to get an orthogonal matrix b<-b+t(b) bb&...

...following matrix: mp <- matrix(c(0,1/4,1/4,3/4,0,1/4,1/4,3/4,1/2),3,3,byrow=T) > mp [,1] [,2] [,3] [1,] 0.00 0.25 0.25 [2,] 0.75 0.00 0.25 [3,] 0.25 0.75 0.50 The eigenvectors of the previous matrix are 1, 0.25 and 0.25 and it is not a diagonalizable matrix. When you try to find the eigenvalues and eigenvectors with R, R responses: > eigen(mp) $values [1] 1.00 -0.25 -0.25 $vectors [,1] [,2] [,3] [1,] 0.3207501 1.068531e-08 -1.068531e-08 [2,] 0.4490502 -7.071068e-01 -7.071068e-01 [3,] 0.8339504 7.071068e-01 7.071068e-01 The eigenvalues are correct but...

Dear all, I am currently working on the calculation of eigenvalues (and -vectors) of large matrices. Since these are mostly sparse matrices and I remember some specific functionalities in MATLAB for sparse matrices, I started a research how to optimize the calculation of eigenvalues of a sparse matrix. The function eigen itself works with the LAPACK library whi...

...way of doing it, however, when I try and calculate a Bray-Curtis distance matrix either using Capscale or Vegedist (capscale I understand uses Vegedist anyway to calculate its distance matrix), R uses up all available memory on the computer, stops and then comes back with errors regarding negative eigenvalues. I must admit to being a very very basic R user so this is starting to go over my head. I tried using the distpcoa program of Legendre and Anderson that can supposedly output a Bray-Curtis distance matrix corrected for the problem of negative eigenvalues (i.e., trying to circumvent the first steps...

Dear R users & Experts, This is just a curiousity, I was wondering why the dominant eigenvetor and eigenvalue of the following matrix is given as the third. I guess this could complicate automatic selection procedures. 0 0 0 0 0 5 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 Please

DeaR list, I happily use eigen() to compute the eigenvalues and eigenvectors of a fairly large matrix (200x200, say), but it seems over-killed as its rank is limited to typically 2 or 3. I sort of remember being taught that numerical techniques can find iteratively decreasing eigenvalues and corresponding orthogonal eigenvectors, which would provide...

Folks: I'm trying to port some code from python over to R, and I'm running into a wall finding R code that can solve a generalized eigenvalue problem following this function model: http://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.eig.html Any ideas? I don't want to call python from within R for various reasons, I'd prefer a "native" R solution if one

Dear all I am so glad the R can provide the efficient calculate about eigenvector and eigenvalue. However, i have some puzzle about the procedure of eigen. Fristly, what kind of procedue does the R utilize such that the eigen are obtained? For example, A=matrix(c(1,2,4,3),2,2) we can define the eigenvalue lamda, such as det | 1-lamda 4 | =0 | 2 3-lamda | then

Let's say I had a matrix like this: library(Ryacas) x<-Sym("x") m<-matrix(c(cos (x), sin(x), -sin(x), cos(x)), ncol=2) How can I use R to obtain the eigenvalues and eigenvectors? Thanks, John [[alternative HTML version deleted]]

Inicio del mensaje reenviado: > De: Arnau Mir <arnau.mir@uib.es> > Fecha: 14 de noviembre de 2011 13:24:31 GMT+01:00 > Para: Martin Maechler <maechler@stat.math.ethz.ch> > Asunto: Re: [R] How to compute eigenvectors and eigenvalues? > > Sorry, but I can't explain very well. > > > The matrix 4*mp is: > > 4*mp > [,1] [,2] [,3] > [1,] 0 1 1 > [2,] 3 0 1 > [3,] 1 3 2 > > > > The eigenvalues are: > lam > [1] 4 -1 -1 > > There is on...

Hello, I have a short question about the prcomp function. First I cite the associated help page (help(prcomp)): "Value: ... SDEV the standard deviations of the principal components (i.e., the square roots of the eigenvalues of the covariance/correlation matrix, though the calculation is actually done with the singular values of the data matrix). ROTATION the matrix of variable loadings (i.e., a matrix whose columns contain the eigenvectors). The function princomp returns this in the element loadings. ..." Now...