numpy.polynomial.legendre.legcompanion

numpy.polynomial.legendre.legcompanion(c)

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.

Parameters :

c : array_like

1-D array of Legendre series coefficients ordered from low to high degree.

Returns :

mat : ndarray

Scaled companion matrix of dimensions (deg, deg).

Notes