# qreig1.s                         J F Monahan, June 2001
 # singular value decomposition of three matrices
# three examples
#  first one
 A <- c( 2, 0, -1, 2, 1, -2.8, -2, 4, 2, .4, 1, 3)
 A <- matrix(A,4,3)
 "first matrix"
 A
 svd(A,4,3)
#  second one
 A <- c( 1, 4, 7, 10, 2, 5, 8, 11, 3, 6, 9, 12)
 A <- matrix(A,4,3)
 "second matrix"
 A
 svd(A,4,3)
#  third and last (and bigger)
 A <- 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)
 A <- matrix(A,8,4)
 "third matrix -- two pairs of equal singular values"
 A
 svd(A,8,4)
 rm(list=ls())