similar to: How to find eigenfunctions and eigenvalues of a fourth order ODE

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,]

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

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 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)

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, 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 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)

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]

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

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.

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 making E <- eigen( something ) I would like to extract those eigenvectors which have an eigenvalue of 1. If I had an isone() function, I would simply say E$vectors[,which(isone(E))] but the problem is that I have no such thing. I found all.equal, so I could test for all.equal(x, 1), but for complex numbers, I need to use something like all.equal(x, 1+0i), don't I? I tried

Dear all: In what I am doing I sometimes get a (Hessian) matrix that has a couple of tiny negative eigenvalues (e.g. -6 * 10^-17). So, I can't run a Cholesky decomp on it - but I need to. Is there an established way to regularize my (Hessian) matrix (e.g., via some transformation) that would allow me to get a semi-positive definite matrix to be used in Cholesky decomp? Or should I try some

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]]

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 which has no special handling for

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

Hi, I have the following problem. It has two parts. 1. I need to calculate the stationary probabilities of a Markov chain, eg if the transition matrix is P, I need x such that xP = x in other words, the left eigenvectors of P which have an eigenvalue of one. Currently I am using eigen(t(P)) and then pick out the vectors I need. However, this seems to be an overkill (I only need a single