1. Orthonormal means X'X = Identity matrix (10 x 10). That means the pairwise correlation coefficients can NOT be different from 0.
2. Not all symmetric matrices with 1's on the diagonal and random numbers U(-1, 1) on the off diagonal are correlation matrices. Consider the following example:
Cormat <- array(c(1, -0.9, -0.9, -0.9, 1, -0.9, -0.9, -0.9, 1), dim=c(3,3))
> Cormat
[,1] [,2] [,3]
[1,] 1.0 -0.9 -0.9
[2,] -0.9 1.0 -0.9
[3,] -0.9 -0.9 1.0
> eigen(Cormat)
$values
[1] 1.9 1.9 -0.8
The fact that one eigenvalue is negative means that this "Cormat" is not positive definite.
hope this helps. spencer graves
rui wrote:
Dear R community:
I want to simulate a regression matrix which
is generated from an orthonormal matrix X of dimension 30*10 with different between-column pairwise correlation coefficients generated from uniform distribution U(-1,1).
Thanks in advance!
Rui [[alternative HTML version deleted]]
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