Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
(5, 6)
sage: all([x in ZZ for x in B_expanded.list()])
True
sage: C=B_expanded.submatrix(0,0,B.nrows()-B.nullity(),B.ncols())
sage: L=B_expanded.submatrix(B.nrows()-B.nullity(),B.ncols())
sage: B.right_kernel()==C.right_kernel()
True
sage: B.row_space()==C.row_space()
True
sage: B.column_space()==L.right_kernel()
True
sage: B.left_kernel()==L.row_space()
True
For more, see the documentation of the random_subspaces_matrix() function. In the notebook or at
the Sage command-line, first execute the following to make this further documentation available:
from sage.matrix.constructor import random_subspaces_matrix
Random unimodular matrices. The algorithm=’unimodular’ keyword, along with an optional entry size
control (upper_bound) will return a matrix of determinant 1. When the base ring is ZZ or QQ the result has
integer entries, whose magnitudes can be limited by the value of upper_bound.
sage: C=random_matrix(QQ, 5, algorithm=’unimodular’, upper_bound=70); C # random
sage: det(C)
1
sage: C.base_ring()
Rational Field
sage: (C.nrows(), C.ncols())
(5, 5)
sage: all([abs(x)