PCA - correlation matrix question

[Martyn Colins <martyncollins10@yahoo.com>]

 

Dear all,

 

Suppose I define the following correlation matrix:

 

my.matrix <- matrix(1, 20, 20)

my.matrix[row(my.matrix) > col(my.matrix)]  <- c(
 0.5, 0.2, 0.1, rep(0.2, 2), 0.15, 0.3, 0.2, 0.3, rep(0.2, 2), rep(0.1, 2), 0.2, rep(0.4, 2), 0, rep(0.2, 2),0.1, 0, 0.2, 0.15, rep(0.1, 3), 0.3, rep(0.15, 2), rep(0, 2), 0.15, rep(0.4, 2), 0, 0.15, 0, 0.2, 0.3, 0, 0.1, rep(0, 2) , 0.1, rep(0, 2), 0.5, 0.2, rep(0, 5), 0.2, 0.3, rep(0.1, 7), 0.3, rep(0.1, 7), rep(0.4, (16*15)/2))
 
my.matrix[row(my.matrix)<col(my.matrix)] <- t(my.matrix)[row(my.matrix)<col(my.matrix)]

 

 

Then I calculate the eigenvectors associated with this correlation matrix:

 

my.pca.vec <- eigen(my.matrix, symmetric=T)$vectors

 

Check to see whether the eigenvectors are independent:

round(crossprod(my.pca.vec),12)

This produces the identity matrix as expected. This should be the same as:

 

round(cor(my.pca.vec), 12)

 

However, this doesn't produce the identity matrix - some of the off-diagonal terms are non-zero.

 

Is this supposed to happen?

 

Thanks in advance for any help.

 

Regards,

Martyn

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