I am new to Eigen. So i wonder whether Eigen offers any function to solve general linear functions with the form: Ax = b.

The relevant entry in the manual:

http://eigen.tuxfamily.org/dox-devel/gr ... apter.html

if A is squared: b = A.lu().solve(b);

Least-square solving with QR: b = A.householderQr().solve(b);

and there are many more options..