scipy.linalg.hessenberg

scipy.linalg.hessenberg(a, calc_q=False, overwrite_a=False)

Compute Hessenberg form of a matrix.

The Hessenberg decomposition is:

A = Q H Q^H

where Q is unitary/orthogonal and H has only zero elements below the first sub-diagonal.

Parameters :

a : ndarray

Matrix to bring into Hessenberg form, of shape (M,M).

calc_q : bool, optional

Whether to compute the transformation matrix. Default is False.

overwrite_a : bool, optional

Whether to overwrite a; may improve performance. Default is False.

Returns :

H : ndarray

Hessenberg form of a, of shape (M,M).

Q : ndarray

Unitary/orthogonal similarity transformation matrix A = Q H Q^H. Only returned if calc_q=True. Of shape (M,M).