[R] a numeric problem

[baicaidoufu]

### An numeric problem in R  ########

###I have two matrix one is##########

A <- matrix(c(21.97844, 250.1960, 2752.033, 29675.88, 316318.4, 3349550,
35336827,
              24.89267, 261.4211, 2691.009, 27796.02, 288738.7, 3011839,
31498784,
              21.80384, 232.3765, 2460.495, 25992.77, 274001.6, 2883756,
30318645,
              39.85801, 392.2341, 3971.349, 40814.22, 423126.2, 4409388,
46090850,
              25.55343, 235.5315, 2343.281, 23987.10, 248557.3, 2590821,
27089162,
              16.63100, 195.4592, 2200.264, 24006.66, 257499.5, 2736200,
28922851,
              23.20258, 262.6086, 2824.971, 29973.61, 316369.1, 3331009,
35025965
              ),7,7,byrow=T)

#### the other one is##################
S<-matrix(c(356.57205,  32.55943, 120.28162,  95.74285,  45.013261,
271.557635, 183.9009,
             32.55943, 299.68103,  81.95644, 246.95280,  96.023270, 
19.383732, 153.4544,
            120.28162,  81.95644, 277.09354,  85.42180, 138.751600,
138.972234, 140.0991,
             95.74285, 246.95280,  85.42180, 527.78444, 182.417527, 
24.946245, 129.1490,
             45.01326,  96.02327, 138.75160, 182.41753, 328.414655,  
1.035543,  63.2730,
            271.55764,  19.38373, 138.97223,  24.94625,   1.035543,
322.635669, 158.5317,
            183.90092, 153.45443, 140.09909, 129.14899,  63.273005,
158.531662, 256.1531
            ),7,7,byrow=T)

####both of these two matrix are non-singular so their inverse should be
exists######
####while 
KK <- t(A)%*%solve(S)%*%A
det(KK) ###12553.48 which is not 0, but solve() function refuse to work now.

##  So I try to use ginv() instead###
ginv(KK)

### It is expected that

A%*%ginv(t(A)%*%solve(S)%*%A)%*%t(A) 

### should equal to solve(S)######

solve(S) 

### but it is not!!!  
### So I am wondering in such situation, do you have any suggestion?
### I have tried the argument "tol = sqrt(.Machine$double.eps))" in ginv(),
but it won't help in 
### more larger determinant matrix.

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