scipy.linalg.null_space#
- scipy.linalg.null_space(A, rcond=None)[source]#
Construct an orthonormal basis for the null space of A using SVD
- Parameters:
- A(M, N) array_like
Input array
- rcondfloat, optional
Relative condition number. Singular values
s
smaller thanrcond * max(s)
are considered zero. Default: floating point eps * max(M,N).
- Returns:
- Z(N, K) ndarray
Orthonormal basis for the null space of A. K = dimension of effective null space, as determined by rcond
Examples
1-D null space:
>>> import numpy as np >>> from scipy.linalg import null_space >>> A = np.array([[1, 1], [1, 1]]) >>> ns = null_space(A) >>> ns * np.sign(ns[0,0]) # Remove the sign ambiguity of the vector array([[ 0.70710678], [-0.70710678]])
2-D null space:
>>> from numpy.random import default_rng >>> rng = default_rng() >>> B = rng.random((3, 5)) >>> Z = null_space(B) >>> Z.shape (5, 2) >>> np.allclose(B.dot(Z), 0) True
The basis vectors are orthonormal (up to rounding error):
>>> Z.T.dot(Z) array([[ 1.00000000e+00, 6.92087741e-17], [ 6.92087741e-17, 1.00000000e+00]])