hessenberg(a, calc_q=False, overwrite_a=False, check_finite=True)
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.
Matrix to bring into Hessenberg form.
Whether to compute the transformation matrix. Default is False.
Whether to overwrite a; may improve performance. Default is False.
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.
Hessenberg form of a.
Unitary/orthogonal similarity transformation matrix A = Q H Q^H
. Only returned if calc_q=True
.
Compute Hessenberg form of a matrix.
>>> 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))) TrueSee :
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.linalg._decomp.hessenberg
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