[R] How to generate regression matrix with correlation matrix

[Spencer Graves]

	  What problem are you really trying to solve?  The problem statement 
as I read it contains two logical contradictions that I see:

	  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]]
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help