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 - ssmaller 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.]])