Dipeptide Inverse Covariance

There is a subtle difference for the order of contructing and inverse a matrix.

1. If contruct a covariance first, then inverse it, the results is showed below

mi

     [,1] [,2]               [,3]               [,4]
[1,]    0  0.0 -3.999999999999993  3.499999999999994
[2,]    0  0.0  2.999999999999995 -2.499999999999996
[3,]   -2  1.5  0.000000000000000  0.000000000000000
[4,]    1 -0.5  0.000000000000000  0.000000000000000

2. But if inverst each block matrix first then contruct a bigger inverse covariance, the results is showed below

m

                   [,1]               [,2] [,3] [,4]
[1,]  0.000000000000000  0.000000000000000   -2  1.5
[2,]  0.000000000000000  0.000000000000000    1 -0.5
[3,] -3.999999999999993  3.499999999999994    0  0.0
[4,]  2.999999999999995 -2.499999999999996    0  0.0

ai

     [,1] [,2]
[1,]   -2  1.5
[2,]    1 -0.5