Definition
Solution is
If such inverse not exists, we need to use from pseudo inverse (Moore-Penrose Inverse) to solve it.
Example of solving polynomial
Given vector and as input and output, we want to find coefficients.
- build Vandermonde matrix
- Solve it by normal equation / pseudo inverse (Moore-Penrose Inverse)
# build Vandermonde matrix
A = np.vander(x, 4, True)
c = la.solve(A.T @ f, A.T @ A)