Inverse of a symmetric matrix is not symmetric?

[rdeits]

PSA: floating-point arithmetic

Sometimes people are surprised by the results of floating-point calculations such as julia> 5/6 0.8333333333333334 # shouldn't the last digit be 3? julia> 2.6 - 0.7 - 1.9 2.220446049250313e-16 # shouldn't the answer be 0? These are not bugs in Julia. They’re consequences of the IEEE-standard 64-bit binary representation of floating-point numbers that is burned into computer hardware, which Julia and many other languages use by default. Brief explanation You can t…

All math performed with floating-point numbers is subject to some degree of round-off and approximation. The inverse of your matrix is not perfectly symmetric, but it is very close:

julia> minv = inv(mat)
6×6 Array{Float64,2}:
  1.18147    -0.502645    0.1883     -0.0692716   0.0250252  -0.0079607
 -0.502645    1.39526    -0.582587    0.217304   -0.0786496   0.0250252
  0.1883     -0.582587    1.42474    -0.59216     0.217304   -0.0692716
 -0.0692716   0.217304   -0.59216     1.42474    -0.582587    0.1883   
  0.0250252  -0.0786496   0.217304   -0.582587    1.39526    -0.502645 
 -0.0079607   0.0250252  -0.0692716   0.1883     -0.502645    1.18147  

julia> minv - minv'
6×6 Array{Float64,2}:
  0.0          -1.11022e-16   2.77556e-17   4.16334e-17  -1.04083e-17   3.46945e-18
  1.11022e-16   0.0          -1.11022e-16  -5.55112e-17   1.38778e-17  -3.46945e-18
 -2.77556e-17   1.11022e-16   0.0           2.22045e-16  -8.32667e-17   1.38778e-17
 -4.16334e-17   5.55112e-17  -2.22045e-16   0.0           1.11022e-16  -5.55112e-17
  1.04083e-17  -1.38778e-17   8.32667e-17  -1.11022e-16   0.0           0.0        
 -3.46945e-18   3.46945e-18  -1.38778e-17   5.55112e-17   0.0           0.0