# scipy.linalg.hessenberg¶

scipy.linalg.hessenberg(a, calc_q=False, overwrite_a=False, check_finite=True)[source]

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 : (M, M) array_like Matrix to bring into Hessenberg form. 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. check_finite : bool, optional Whether to check that the input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs. H : (M, M) ndarray Hessenberg form of a. Q : (M, M) ndarray Unitary/orthogonal similarity transformation matrix A = Q H Q^H. Only returned if calc_q=True.

Examples

>>> from scipy.linalg import hessenberg
>>> A = np.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]])
>>> H, Q = hessenberg(A, calc_q=True)
>>> H
array([[  2.        , -11.65843866,   1.42005301,   0.25349066],
[ -9.94987437,  14.53535354,  -5.31022304,   2.43081618],
[  0.        ,  -1.83299243,   0.38969961,  -0.51527034],
[  0.        ,   0.        ,  -3.83189513,   1.07494686]])
>>> np.allclose(Q @ H @ Q.conj().T - A, np.zeros((4, 4)))
True


#### Previous topic

scipy.linalg.rsf2csf

#### Next topic

scipy.linalg.cdf2rdf