# [R] B %*% t(B) = R , then solve for B

Doran, Harold HDoran at air.org
Tue Apr 12 18:10:46 CEST 2011

```I gave you a solution for the triangular matrix. Can you explain why that is not what you need?

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
> Behalf Of Shawn Koppenhoefer
> Sent: Tuesday, April 12, 2011 11:37 AM
> To: r-help at r-project.org
> Subject: Re: [R] B %*% t(B) = R , then solve for B
> Importance: High
>
> BTW,
> The same solution can be found using SVD (Singular Value Decomposition)
>
> example,
>
> ## Define the matrix that we want to decompose into the product of a
> matrix and its transform
> 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)
>
> ## Compute the singular-value decomposition, and construct F from its pieces
> SVD=svd(M, nu=3, nv=3)
> U=SVD\$u
> D=diag(SVD\$d)
> V=SVD\$v
> U %*% D %*% t(V)
> F = U %*% sqrt(diag(SVD\$d))
>
> ## Test to see of the product of F with its transpose is equal to M
> 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
>
>
> /Shawn
>
>
> p.s.
> HOWEVER I would still like to find a solution that gives me a diagonal
> matrix for F.
> For example, I would like this result:,
>
>      > F
>            [,1]   [,2]  [,3]
>     [1,] 0.781  0.000 0.000
>     [2,] 0.328  0.637 0.000
>     [3,] 0.238 -0.341 0.873
>
>
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help