Spectral decomposition (eigen)

Question

i have a problem with calculation the Spectral decomposition, i guess, with the sorting of eigen.

According to this website http://www.deltaquants.com/cleaning-correlation-matrices.html i would like to do the same calculation in R

Input <- data.frame(read.csv2(file="testmatrix.csv", header=FALSE, sep=";"))
# same matrix as the example on the website
Eigen <- eigen(Input, only.values=FALSE, symmetric = TRUE)

#Get the eigenvalues/eigenvectors
Eigen$values
Eigen$vectors

The result on the website (excel):

The result from eigen (R)

As the result the new correlation matrix C is not correct.

Thanks for the help. I could provide further information e.c. Code or more details - if it helps.

Answer 1

If you want to order the eigenvalue of a matrix in increasing order, just index eigenvectors and eigenvalues with the output of the order function:

mat <- matrix(c(1, 2, 3, 2, 7, 4, 3, 4, 0), nrow=3)
e <- eigen(mat)
o <- order(e$values, decreasing=FALSE)
e$values[o]
# [1] -2.961797  1.056689  9.905108
e$vectors[,o]
#            [,1]       [,2]       [,3]
# [1,]  0.5110650  0.7915817 -0.3349790
# [2,]  0.2299503 -0.5014262 -0.8340831
# [3,] -0.8282122  0.3492421 -0.4382859

Answer 2

The eigenvalues are in a different order. Both results are correct.

Note that it is accepted practice to order the eigenvalues according to nonincreasing absolute value, as is returned by R, but not by Excel. So if one answer is "wrong," it is Excel's.