companion(a)

Create the companion matrix associated with the polynomial whose coefficients are given in a.

Notes

Parameters

a : (N,) array_like

1-D array of polynomial coefficients. The length of a must be at least two, and a[0] must not be zero.

Raises

ValueError

If any of the following are true: a) a.ndim != 1 ; b) a.size < 2 ; c) a[0] == 0 .

Returns

c : (N-1, N-1) ndarray

The first row of c is -a[1:]/a[0] , and the first sub-diagonal is all ones. The data-type of the array is the same as the data-type of 1.0*a[0] .

Create a companion matrix.

Examples

>>> from scipy.linalg import companion
... companion([1, -10, 31, -30])
array([[ 10., -31.,  30.],
       [  1.,   0.,   0.],
       [  0.,   1.,   0.]])

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.linalg._special_matrices.companion scipy.linalg._special_matrices.fiedler_companion

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GitHub : /scipy/linalg/_special_matrices.py#552
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