Computational cost of function eig

I am wondering what is the computational cost (using asymptotic notation) of function eig in MatLab r2016, and what algorithm is used to compute the diagonal matrix and the change of basis matrix. In this discussion http://it.mathworks.com/matlabcentral/answers/10335-computational-complexity-of-eig-and-pinv it says it is something around O(n^3), or maybe something less, but why? Thank you in advance

[Adam]

You can estimate this roughly for yourself simply by running a test on different sizes of input. If you are able to look inside the code by simply opening the file then you will be able to see what algorithm is used. If you can't then it is likely because it is proprietary Mathworks code.

[Walter Roberson]

It depends on the properties of the matrix whose eigenvalues are being taken.

[Viviana Arrigoni]

What if the matrix is symmetric?

Answer 1

[Walter Roberson]

https://en.m.wikipedia.org/wiki/Eigenvalue_algorithm

[Walter Roberson]

You should probably assume that for sufficiently large arrays that MATLAB invokes one of the below routines:

http://www.netlib.org/lapack/double/