intersections

intersections.column_space_intersection(*As, tol, orthonormal=False)

Return a matrix with orthonormal columns spanning the intersection of the column spaces of the given matrices.

INPUT:

  • *As – matrices with a fixed number of rows and linearly independent (or orthonormal) columns each

  • tol – tolerance for truncating the singular values to determine the rank of the intersection

  • orthonormal – boolean (default: False); if True, the columns of each matrix are assumed to be orthonormal

ALGORITHM: Golub, van Loan – Algorithm 12.4.3

intersections.null_space_intersection(*As, tol)

Return a matrix with orthonormal columns spanning the intersection of the null spaces of the given matrices.

INPUT:

  • *As – matrices with a fixed number of columns

  • tol – tolerance for truncating the singular values to determine the rank of intermediate results

ALGORITHM: Golub, van Loan – Algorithm 12.4.2

intersections.null_space(A, tol)