similar to: How to determine the number of dominant eigenvalues in PCA

Hi, Given a positive integer N, and a real number \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

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 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 eigenvalues but different to the R ones. For real

Dear all, I have read various descriptions of employing resampling techniques, such as the bootstrap, to estimate the uncertainties of the eigenvectors computed by PCA. When I try

Hi There, I'm working on some cluster analyses on a large data-set using hclust with Wards method and Manhattan (city block) distance measures. I've created dendrograms to illustrate the clustering criteria, but would like to create a plot to examine for the classic elbow criterion to use in determining the best number of clusters. Ideally I'd like to plot percent variance explained

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'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 #defining the matrix

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 Office: 425BSW rlyoung at email.arizona.edu (520) 621-4005

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

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

Dear All I am trying to do a partial canonical analysis of principal coordinates using Bray-Curtis distances. The capscale addin to R appears to be the only 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,

Hello. Consider the 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]

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]]

Hi, is there any other routine for factor analysis in R then factanal? Basically I'am interested in another extraction method then the maximum likelihood method and looking for unweighted least squares. Thanks in advance Sigbert Klinke

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 a nice alternative (once I have the

I need to compute generalized eigenvalues. The eigen function in base doesn't do it and I can't find a package that does. As I understand it, Lapack __can__ computer them (http://www.netlib.org/lapack/lawn41/node111.html) and R can use Lapack. If there is no function already, can I access Lapack from R and use those routines directly? Thank you, Joshua Gilbert.

I thought that the function eigen(A) will return a matrix with eigenvectors that are independent of each other (thus forming a base and the matrix being invertible). This seems not to be the case in the following example A=matrix(c(1,2,0,1),nrow=2,byrow=T) eigen(A) ->ev solve(ev$vectors) note that I try to get the upper triangular form with eigenvalues on the diagonal and (possibly) 1 just

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<-eigen(b,symmetric=T)

Hi, I want to know whether there is any function in R to find STRESS after using cmdscale and estimating the coordinates, I have written these functions to find stress (for p =1,2,3,4,5) stress<-rep(0,5) for(p in 1:5) { datahat<-cmdscale(d,p) deltahat<-as.matrix(dist(datahat)) a<-0 b<-0 for(i in 1:n) { for(j in 1:n) { a<-d[i,j]^2+a b<-(d[i,j]-deltahat[i,j])^2+b } }

After doing a PCA using princomp, how do you view how much each component contributes to variance in the dataset. I'm still quite new to the theory of PCA - I have a little idea about eigenvectors and eigenvalues (these determine the variance explained?). Are the eigenvalues related to loadings in R? Thanks, Paul -- View this message in context: