Hello.
I found a solution that may interest others.
Recall that my problem was how to use R to decompose a matrix into the
product of a matrix and its transpose. or, symbolically:
For known matrix M (3x3 matrix) and unknown matrix F and its
transpose t(F)
where F * t(F) = M
determine F
The solution using R seems to be :
U=eigen(M)$vectors
D=diag(x=eigen(M)$values)
F=U %*% sqrt(D)
But now I have two new questions:
1. How can I find a solution where F is a triangular matrix.
2. How can I find solutions to non-square matrices?
/shawn
p.s. Here's a numerical example that demonstrates the above.
> M
[,1] [,2] [,3]
[1,] 0.6098601 0.2557882 0.1857773
[2,] 0.2557882 0.5127065 -0.1384238
[3,] 0.1857773 -0.1384238 0.9351089
> U=eigen(M)$vectors
> D=diag(x=eigen(M)$values)
> F=U %*% sqrt(D)
> *F %*% t(F)*
[,1] [,2] [,3]
[1,] 0.6098601 0.2557882 0.1857773
[2,] 0.2557882 0.5127065 -0.1384238
[3,] 0.1857773 -0.1384238 0.9351089
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