Return the scaled companion matrix of c.
The basis polynomials are scaled so that the companion matrix is symmetric when c is an Legendre basis polynomial. This provides better eigenvalue estimates than the unscaled case and for basis polynomials the eigenvalues are guaranteed to be real if numpy.linalg.eigvalsh is used to obtain them.
c : array_like
1-D array of Legendre series coefficients ordered from low to high degree.
mat : ndarray
Scaled companion matrix of dimensions (deg, deg).