[R] eigenvalues and correlation matrices

[dM/]

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. The
results don't indicate any problems, but I thought I'd cross check the
syntax by assessing the eigen values of the following simple 3 x 3
matrix:

row 1) 2,1,1
row 2) 1,3,2
row 3) -1,1,2

The eigenvalues for this matrix are: 1,2 and 4.  I have confirmed this
using the following site:
http://www.akiti.ca/Eig3Solv.html

However, when I run my code in R (see below), I get different
answers.  What gives?

#test std 3 x 3:
  setwd("S:/790/Actuarial/Computing and VBA/R development/
Eigenvalues")
  testmatrix<-data.frame(read.csv("threeBythree.csv",header=FALSE))

  testmatrix

#check that the matrix drawn in is correct
  nrow(testmatrix)
  ncol(testmatrix)

#calculate the eigenvalues
  eigen(testmatrix,symmetric = TRUE,only.value=TRUE)