similar to: how to invert the matrix with quite small eigenvalues

Hi, It is my understanding that the eigenvectors of a circulant matrix are given as follows: 1,omega,omega^2,....,omega^{p-1} where the matrix has dimension given by p x p and omega is one of p complex roots of unity. (See Bellman for an excellent discussion on this). The matrix created by the attached row and obtained using the following commands indicates no imaginary parts for the

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. 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 R-users, Is there a preferred method for testing whether a real symmetric matrix is positive definite? [modulo machine rounding errors.] The obvious way of computing eigenvalues via "E <- eigen(A, symmetric=T, only.values=T)$values" and returning the result of "!any(E <= 0)" seems less efficient than going through the LU decomposition invoked in

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

1. Martin Maechler's comments should be taken as replacements for anything I wrote where appropriate. Any apparent conflict is a result of his superior knowledge. 2. 'eigen' returns the eigenvalue decomposition assuming the matrix is symmetric, ignoring anything in m[upper.tri(m)]. 3. The basic idea behind both posdefify and nearPD is to compute the

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 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

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

Looks like the files did not go through again. In any case, here is the kinv: please cut and paste and save to a file: -1.16801E-03 -2.24310E-03 -1.16864E-03 -2.24634E-03 -1.17143E-03 -2.25358E-03 -1.17589E-03 -2.26484E-03 -1.18271E-03 -2.27983E-03 -1.19124E-03 -2.29896E-03 -1.20164E-03 -2.32206E-03 -1.21442E-03 -2.34911E-03 -1.22939E-03 -2.38073E-03

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

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

Hello list, Sorry, these questions are not directly linked to R. If I consider an indefinte real matrix, I would like to know if the symmetry of the matrix is sufficient to say that their eigenvectors are real ? And what is the conditions to ensure that eigenvectors are real in the case of an asymmetric matrix (if some conditions exist)? Thanks in Advance, St?phane DRAY

Dear all R users, Can anyone tell me to calculate Eigen value of any real symmetric matrix which algorithm R uses? Is it Jacobi method ? If not is it possible to get explicit algorithm for calculating it? Thanks and regards, Arun [[alternative HTML version deleted]]

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, It is not a R related problem rather than statistical/mathematical. However I am posting this query hoping that anyone can help me on this matter. My problem is to get the Geometrical Interpretation of Eigen value and Eigen vector of any square matrix. Can anyone give me a light on it? Thanks and regards, Arun [[alternative HTML version deleted]]

Can someone confirm that the EISPACK routines for eigenvalues of symmetric matrix are in base R. They seem to be, but I can't seem to locate where they are in the src tree. Thanks. Chong Gu -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or

Dear R users, even if this question is not related to an issue about R, probably some of you will be able to help me. I have a square matrix of dimension k by k with alpha on the diagonal and beta everywhee else. This symmetric matrix is called symmetric compound matrix and has the form a( I + cJ), where I is the k by k identity matrix J is the k by k matrix of all ones a = alpha - beta c =

Dear all, Has someone implemented in R (or any other language) Knol DL, ten Berge JMF. Least-squares approximation of an improper correlation matrix by a proper one. Psychometrika, 1989, 54, 53-61. or any other similar algorithm? Best regards Jens Oehlschl?gel Background: I want to factanal() matrices of polychoric correlations which have negative eigenvalue. I coded Highham 2002