# rsvd.r         
 #
 # compute singular values and vectors 
 #
 # first matrix
   A <- matrix(c(2,0,-1,2,1,-2.8,-2,4,2,.4,1,3),4,3)
   A
   svdA <- svd(A)
   svdA
   t(svdA$u) %*% A %*% svdA$v       # diagonal?
 # second matrix
   A <- matrix(1:12,4,3,byrow=T)
   A
   svdA <- svd(A)
   svdA
   t(svdA$u) %*% A %*% svdA$v       # diagonal?
 # third matrix
   A <- matrix(c(1,1,2,1,1,-1,0,0, 3,6,9,12,0,0,0,0, -1,1,0,0,1,1,2,1,
          0,0,0,0,3,6,9,12),8,4)
   A
   svdA <- svd(A)
   svdA
   t(svdA$u) %*% A %*% svdA$v       # diagonal?
 # done
   rm(list=ls())
   q()