# rank_nullspace¶

quantecon.rank_nullspace.nullspace(A, atol=1e-13, rtol=0)[source]

Compute an approximate basis for the nullspace of A.

The algorithm used by this function is based on the singular value decomposition of A.

Parameters: A : array_like(float, ndim=1 or 2) A should be at most 2-D. A 1-D array with length k will be treated as a 2-D with shape (1, k) atol : scalar(float), optional(default=1e-13) The absolute tolerance for a zero singular value. Singular values smaller than atol are considered to be zero. rtol : scalar(float), optional(default=0) The relative tolerance. Singular values less than rtol*smax are considered to be zero, where smax is the largest singular value. ns : array_like(float, ndim=2) If A is an array with shape (m, k), then ns will be an array with shape (k, n), where n is the estimated dimension of the nullspace of A. The columns of ns are a basis for the nullspace; each element in numpy.dot(A, ns) will be approximately zero. Note: If both atol and rtol are positive, the combined tolerance is the maximum of the two; that is: tol = max(atol, rtol * smax) Note: Singular values smaller than tol are considered to be zero.
quantecon.rank_nullspace.rank_est(A, atol=1e-13, rtol=0)[source]

Estimate the rank (i.e. the dimension of the nullspace) of a matrix.

The algorithm used by this function is based on the singular value decomposition of A.

Parameters: A : array_like(float, ndim=1 or 2) A should be at most 2-D. A 1-D array with length n will be treated as a 2-D with shape (1, n) atol : scalar(float), optional(default=1e-13) The absolute tolerance for a zero singular value. Singular values smaller than atol are considered to be zero. rtol : scalar(float), optional(default=0) The relative tolerance. Singular values less than rtol*smax are considered to be zero, where smax is the largest singular value. r : scalar(int) The estimated rank of the matrix. Note: If both atol and rtol are positive, the combined tolerance is the maximum of the two; that is: tol = max(atol, rtol * smax) Note: Singular values smaller than tol are considered to be zero.

numpy.linalg.matrix_rank