numpy.polynomial.legendre.legcompanion — NumPy v2.2 Manual (original) (raw)

polynomial.legendre.legcompanion(c)[source]#

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 ifnumpy.linalg.eigvalsh is used to obtain them.

Parameters:

carray_like

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

Returns:

matndarray

Scaled companion matrix of dimensions (deg, deg).