Let A be a real symmetric $(N\times N)$ matrix.
Although I would like to check its rank and determinant in order to calculate the inverse of A, a confliction arised. $\\$ Since A is a large matrix, (I wish I could break the matrix in several small pieces and have a look), I checked the rank and the determinant through MATLAB.
Though the rank is N, the determinant is equal to 0.
>> rank(A) ans = N >> det(A) ans = 0 >> cond(A) ans = 5.2e+05
As far as I know that the full rank is identical to be invertable, but it cannot since the determinant is zero. How it can be resolved? Thank you in advance.