Linear Algebra

hermitian(A)	Returns the Hermitian transpose of a matrix
AH_v(A, v)	Returns \(A^H v\) for a given matrix A and a vector v

Triangular Systems

solve_Lx_b(L, b)	Solves the system L x = b using back substitution
solve_LTx_b(L, b)	Solves the system L^T x = b using back substitution
solve_Ux_b(U, b)	Solves the system U x = b using back substitution
solve_UTx_b(U, b)	Solves the system U^T x = b using back substitution
solve_spd_chol(L, b)	Solves a symmetric positive definite system A x = b where A = L L’

Fundamental Subspaces

orth(A[, rcond])	Constructs an orthonormal basis for the range of A using SVD
row_space(A[, rcond])	Constructs an orthonormal basis for the row space of A using SVD
null_space(A[, rcond])	Constructs an orthonormal basis for the null space of A using SVD
left_null_space(A[, rcond])	Constructs an orthonormal basis for the left null space of A using SVD

Singular Value Decomposition

effective_rank(A[, rcond])	Returns the effective rank of A based on its singular value decomposition
effective_rank_from_svd(u, s, vh[, rcond])	Returns the effective rank of a matrix from its SVD
singular_values(A)	Returns the singular values of a matrix

Subspaces

project_to_subspace(U, v)	Projects a vector to a subspace
is_in_subspace(U, v)	Checks whether a vector v is in the subspace spanned by an ONB U or not
principal_angles_cos(A, B)	Returns the cosines of principal angles between two subspaces
principal_angles_rad(A, B)	Returns the principal angles between two subspaces in radians
principal_angles_deg(A, B)	Returns the principal angles between two subspaces in degrees
smallest_principal_angle_cos(A, B)	Returns the cosine of smallest principal angle between two subspaces
smallest_principal_angle_rad(A, B)	Returns the smallest principal angle between two subspaces in radians
smallest_principal_angle_deg(A, B)	Returns the smallest principal angle between two subspaces in degrees
smallest_principal_angles_cos(subspaces)	Returns the smallest principal angles between each pair of subspaces
smallest_principal_angles_rad(subspaces)	Returns the smallest principal angles between each pair of subspaces in radians
smallest_principal_angles_deg(subspaces)	Returns the smallest principal angles between each pair of subspaces in degrees
subspace_distance(A, B)	Returns the Grassmannian distance between two subspaces