Solution found...
Sorry for not having known this,...
Apparently, what I was after is called a "Choleski factorization".
The solution pops right out of R, as follows:
> M<-matrix(c(0.6098601, 0.2557882, 0.1857773,
+ 0.2557882, 0.5127065, -0.1384238,
+ 0.1857773, -0.1384238, 0.9351089 ),
+ nrow=3, ncol=3, byrow=TRUE)
> chol(M)
[,1] [,2] [,3]
[1,] 0.7809354 0.3275408 0.2378907
[2,] 0.0000000 0.6367288 -0.3397722
[3,] 0.0000000 0.0000000 0.8735398
>
Thanks again for all your help!
/shawn
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