svd and eigen

A<-matrix(rnorm(10),2,5)
svd(A)$d

eigen(A%*%t(A))$values^0.5

Hello List,
i need help for eigen and svd functions. I have a non-symmetric 
square matrix. These matrix is not positive (some eigenvalues are 
negative). I want to diagonalise these matrix. So, I use svd and 
eigen and i compare the results. eigen give me the "good" eigenvalues 
(positive and negative). I compare with another software and the 
results are the same. BUT, when i use svd, the results are completely 
different (no sign and not the same value). I thought that svd is a 
generalisation of eigen for non-square matrices but apparently, there 
are more differences ?
I 've R1.2.3 on W2000.

The singular values of a matrix A are the +ve square roots of
the eigenvalues of A'A, or AA' (depending on the shape of A), where A' is
transpose of A. e.g....

 A<-matrix(rnorm(10),2,5)
 svd(A)$d

[1] 1.6157235 0.9652578

 eigen(A%*%t(A))$values^0.5

[1] 1.6157235 0.9652578

 svd(mat)$d

 eigen(mat)$values

The singular values of a matrix A are the +ve square roots of
the eigenvalues of A'A, or AA' (depending on the shape of A), where A' is
transpose of A. e.g....

 A<-matrix(rnorm(10),2,5)
 svd(A)$d

[1] 1.6157235 0.9652578

 eigen(A%*%t(A))$values^0.5

[1] 1.6157235 0.9652578

Yes, of course ... but :

 svd(mat)$d

  [1] 1.17069725 1.01156192 0.90637068 0.81183730 0.75508662
0.57540484 0.53941772 0.51359072 0.49338327 0.45236340
[11] 0.42074523 0.40355803 0.37502763 0.36161939 0.31022290 0.30024633
0.27126673 0.25990555 0.19974930 0.18071039
[21] 0.14214615 0.13599764 0.09270370 0.06966780 0.04571913

 eigen(mat)$values

  [1]  1.00000000  0.89480696  0.79123824  0.69792179 -0.63442305
-0.55072855 -0.52263267  0.50820449 -0.50552311
[10] -0.45431956 -0.40717371  0.37976933 -0.36275320  0.34892256
-0.34126875 -0.31841576 -0.30411335  0.27663288
[19] -0.22103895 -0.19623454 -0.14990290  0.14228531 -0.10127212
0.08101399 -0.05099532