Module: sage.matrix.matrix_space
Module-level Functions
base_ring, nrows, [ncols=False], [sparse=None]) |
Create with the command
MatrixSpace(base_ring , nrows [, ncols] [, sparse])
The default value of the optional argument sparse is False. The default value of the optional argument ncols is nrows.
INPUT: base_ring -- a ring nrows -- int, the number of rows ncols -- (default nrows) int, the number of columns sparse -- (default false) whether or not matrices are given a sparse representation OUTPUT: The space of all nrows x ncols matrices over base_ring.
sage: MS = MatrixSpace(RationalField(),2) sage: MS.base_ring() Rational Field sage: MS.dimension() 4 sage: MS.dims() (2, 2) sage: B = MS.basis() sage: B [[1 0] [0 0], [0 1] [0 0], [0 0] [1 0], [0 0] [0 1]] sage: B[0] [1 0] [0 0] sage: B[1] [0 1] [0 0] sage: B[2] [0 0] [1 0] sage: B[3] [0 0] [0 1] sage: A = MS.matrix([1,2,3,4]) sage: A [1 2] [3 4] sage: MS2 = MatrixSpace(RationalField(),2,3) sage: B = MS2.matrix([1,2,3,4,5,6]) sage: A*B [ 9 12 15] [19 26 33]
sage: M = MatrixSpace(Z, 10) sage: M Full MatrixSpace of 10 by 10 dense matrices over Integer Ring sage: loads(M.dumps()) == M True
x) |
Class: MatrixSpace_domain
self, base_ring, nrows, [ncols=False], [sparse=None]) |
Special Functions: _get_matrix_class
Class: MatrixSpace_field
self, base_field, nrows, [ncols=False], [sparse=None]) |
Functions: base_field
Special Functions: _get_matrix_class
Class: MatrixSpace_generic
self, base_ring, nrows, [ncols=False], [sparse=None]) |
Functions: base_ring,
basis,
dimension,
dims,
gen,
identity_matrix,
is_dense,
is_sparse,
matrix,
matrix_space,
ncols,
ngens,
nrows,
random_element
self, [x=True], [coerce_entries=True], [copy=0]) |
Create a matrix in self. The entries can be specified either as a single list of length nrows*ncols, or as a list of lists.
sage: Z = IntegerRing() sage: M = MatrixSpace(Z,2) sage: M([[1,0],[0,-1]]) [ 1 0] [ 0 -1] sage: M([1,0,0,-1]) [ 1 0] [ 0 -1]
self, [X=True], [prob=1.0], [coerce=[-2, -1, 1, 2]]) |
Returns a random element of self.
Special Functions: __call__,
__cmp__,
__repr__,
_coerce_,
_get_matrix_class,
_latex_
Class: MatrixSpace_pid
self, base_ring, nrows, [ncols=False], [sparse=None]) |
Special Functions: _get_matrix_class
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