scipy.linalg.

orth#

scipy.linalg.orth(A, rcond=None)[source]#

Construct an orthonormal basis for the range of A using SVD

The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details.

Parameters:

A(M, N) array_like: Input array
rcondfloat, optional: Relative condition number. Singular values s smaller than rcond * max(s) are considered zero. Default: floating point eps * max(M,N).

Returns:

Q(M, K) ndarray: Orthonormal basis for the range of A. K = effective rank of A, as determined by rcond

See also

svd: Singular value decomposition of a matrix
null_space: Matrix null space

Examples

>>> import numpy as np
>>> from scipy.linalg import orth
>>> A = np.array([[2, 0, 0], [0, 5, 0]])  # rank 2 array
>>> orth(A)
array([[0., 1.],
       [1., 0.]])
>>> orth(A.T)
array([[0., 1.],
       [1., 0.],
       [0., 0.]])