Sage Reference Manual: Matrices and Spaces of Matrices

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.2gen(n)Return the n-th generator of this matrix space.This doesn’t compute all basis matrices, so it is reasonably intelligent.EXAMPLES:sage: M = Mat(GF(7),10000,5); M.ngens()50000sage: a = M.10sage: a[:4][0 0 0 0 0][0 0 0 0 0][1 0 0 0 0][0 0 0 0 0]get_action_impl(S, op, self_on_left)x.__init__(...) initializes x; see help(type(x)) for signatureidentity_matrix()Returns the identity matrix in self.self must be a space of square matrices. The returned matrix is immutable. Please use copy if you wanta modified copy.EXAMPLES:sage: MS1 = MatrixSpace(ZZ,4)sage: MS2 = MatrixSpace(QQ,3,4)sage: I = MS1.identity_matrix()sage: I[1 0 0 0][0 1 0 0][0 0 1 0][0 0 0 1]sage: Er = MS2.identity_matrix()Traceback (most recent call last):...TypeError: self must be a space of square matricesTESTS:sage: MS1.one()[1,2] = 3Traceback (most recent call last):...ValueError: matrix is immutable; please change a copy instead (i.e., use copy(M) to change ais_dense()Returns True if matrices in self are dense and False otherwise.EXAMPLES:sage: Mat(RDF,2,3).is_sparse()Falsesage: Mat(RR,123456,22,sparse=True).is_sparse()Trueis_finite()EXAMPLES:sage: MatrixSpace(GF(101), 10000).is_finite()True7