Sage Reference Manual: Matrices and Spaces of Matrices

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.2sage: d[(1,1)] = 2sage: dict_to_list(d, 2, 2)[1, 0, 0, 2]sage: dict_to_list(d, 2, 3)[1, 0, 0, 0, 2, 0]sage.matrix.matrix_space.is_MatrixSpace(x)Returns True if self is an instance of MatrixSpace returns false if self is not an instance of MatrixSpaceEXAMPLES:sage: from sage.matrix.matrix_space import is_MatrixSpacesage: MS = MatrixSpace(QQ,2)sage: A = MS.random_element()sage: is_MatrixSpace(MS)Truesage: is_MatrixSpace(A)Falsesage: is_MatrixSpace(5)Falsesage.matrix.matrix_space.list_to_dict(entries, nrows, ncols, rows=True)Given a list of entries, create a dictionary whose keys are coordinate tuples and values are the entries.EXAMPLES:sage: from sage.matrix.matrix_space import list_to_dictsage: d = list_to_dict([1,2,3,4],2,2)sage: d[(0,1)]2sage: d = list_to_dict([1,2,3,4],2,2,rows=False)sage: d[(0,1)]3sage.matrix.matrix_space.test_trivial_matrices_inverse(ring, sparse=True, checkrank=True)Tests inversion, determinant and is_invertible for trivial matrices.This function is a helper to check that the inversion of trivial matrices (of size 0x0, nx0, 0xn or 1x1) is handledconsistently by the various implementation of matrices. The coherency is checked through a bunch of assertions.If an inconsistency is found, an AssertionError is raised which should make clear what is the problem.INPUT:•ring - a ring•sparse - a boolean•checkrank - a booleanOUTPUT:•nothing if everything is correct, otherwise raise an AssertionErrorThe methods determinant, is_invertible, rank and inverse are checked for• the 0x0 empty identity matrix• the 0x3 and 3x0 matrices• the 1x1 null matrix [0]• the 1x1 identity matrix [1]13