The module matrix.matrix_space defines the following methods:
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]
The module matrix.matrix_space defines the following classes: