Index

A

act_on_polynomial() (sage.matrix.matrix0.Matrix method) add() (sage.matrix.matrix_window.MatrixWindow method) add_column() (in module sage.matrix.matrix_integer_dense_hnf) add_column_fallback() (in module sage.matrix.matrix_integer_dense_hnf) add_multiple_of_column() (sage.matrix.matrix0.Matrix method) add_multiple_of_row() (sage.matrix.matrix0.Matrix method) add_prod() (sage.matrix.matrix_window.MatrixWindow method) add_row() (in module sage.matrix.matrix_integer_dense_hnf) adjoint() (sage.matrix.matrix2.Matrix method)

anticommutator() (sage.matrix.matrix0.Matrix method) antitranspose() (sage.matrix.matrix_dense.Matrix_dense method) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method) (sage.matrix.matrix_sparse.Matrix_sparse method) apply_map() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_sparse.Matrix_sparse method) apply_morphism() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_sparse.Matrix_sparse method) arguments() (sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense method) as_bipartite_graph() (sage.matrix.matrix2.Matrix method) as_sum_of_permutations() (sage.matrix.matrix2.Matrix method) augment() (sage.matrix.matrix1.Matrix method) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_mod2_dense.Matrix_mod2_dense method) (sage.matrix.matrix_mod2e_dense.Matrix_mod2e_dense method) (sage.matrix.matrix_sparse.Matrix_sparse method) automorphisms_of_rows_and_columns() (sage.matrix.matrix2.Matrix method)

B

base_extend() (sage.matrix.matrix_space.MatrixSpace method) base_ring() (sage.matrix.matrix0.Matrix method) basis() (sage.matrix.matrix_space.MatrixSpace method) benchmark_hnf() (in module sage.matrix.matrix_integer_dense_hnf) benchmark_magma_hnf() (in module sage.matrix.matrix_integer_dense_hnf)

berlekamp_massey() (in module sage.matrix.berlekamp_massey) BKZ() (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) block_diagonal_matrix() (in module sage.matrix.constructor) block_matrix() (in module sage.matrix.constructor) block_sum() (sage.matrix.matrix1.Matrix method)

C

C (sage.matrix.matrix2.Matrix attribute) cached_method() (sage.matrix.matrix_space.MatrixSpace method) change_names() (sage.matrix.operation_table.OperationTable method) change_ring() (sage.matrix.matrix0.Matrix method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method) (sage.matrix.matrix_space.MatrixSpace method) (sage.matrix.matrix_sparse.Matrix_sparse method) characteristic_polynomial() (sage.matrix.matrix2.Matrix method) charpoly() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense method) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_modn_dense_double.Matrix_modn_dense_template method) (sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method) (sage.matrix.matrix_sparse.Matrix_sparse method) (sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense method) charpoly_GF() (in module sage.matrix.benchmark) charpoly_ZZ() (in module sage.matrix.benchmark) cholesky() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) cling() (sage.matrix.matrix_mod2e_dense.Matrix_mod2e_dense method) cmp_pivots() (in module sage.matrix.matrix2) (in module sage.matrix.misc) codomain() (sage.matrix.action.MatrixMulAction method) coefficient_bound() (sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense method)

column() (sage.matrix.matrix1.Matrix method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method) column_keys() (sage.matrix.operation_table.OperationTable method) column_matrix() (in module sage.matrix.constructor) column_module() (sage.matrix.matrix2.Matrix method) column_space() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_space.MatrixSpace method) columns() (sage.matrix.matrix1.Matrix method) commutator() (sage.matrix.matrix0.Matrix method) companion_matrix() (in module sage.matrix.constructor) condition() (sage.matrix.matrix_double_dense.Matrix_double_dense method) conjugate() (sage.matrix.matrix2.Matrix method) conjugate_transpose() (sage.matrix.matrix2.Matrix method) construction() (sage.matrix.matrix_space.MatrixSpace method) cyclic_subspace() (sage.matrix.matrix2.Matrix method)

D

decomp_seq() (in module sage.matrix.matrix2) decomposition() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method) decomposition_of_subspace() (sage.matrix.matrix2.Matrix method) delete_columns() (sage.matrix.matrix1.Matrix method) delete_rows() (sage.matrix.matrix1.Matrix method) denominator() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method) (sage.matrix.matrix_rational_sparse.Matrix_rational_sparse method) dense_columns() (sage.matrix.matrix1.Matrix method) dense_matrix() (sage.matrix.matrix1.Matrix method) (sage.matrix.matrix_rational_sparse.Matrix_rational_sparse method) dense_rows() (sage.matrix.matrix1.Matrix method) density() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_mod2_dense.Matrix_mod2_dense method) (sage.matrix.matrix_modn_sparse.Matrix_modn_sparse method) (sage.matrix.matrix_sparse.Matrix_sparse method) derivative() (sage.matrix.matrix2.Matrix method) det() (sage.matrix.matrix2.Matrix method) det_from_modp_and_divisor() (in module sage.matrix.matrix_integer_dense_hnf) det_GF() (in module sage.matrix.benchmark) det_given_divisor() (in module sage.matrix.matrix_integer_dense_hnf)

det_hilbert_QQ() (in module sage.matrix.benchmark) det_padic() (in module sage.matrix.matrix_integer_dense_hnf) det_QQ() (in module sage.matrix.benchmark) det_ZZ() (in module sage.matrix.benchmark) determinant() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_mod2_dense.Matrix_mod2_dense method) (sage.matrix.matrix_modn_dense_double.Matrix_modn_dense_template method) (sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template method) (sage.matrix.matrix_mpolynomial_dense.Matrix_mpolynomial_dense method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method) (sage.matrix.matrix_sparse.Matrix_sparse method) diagonal() (sage.matrix.matrix2.Matrix method) diagonal_matrix() (in module sage.matrix.constructor) dict() (sage.matrix.matrix0.Matrix method) dict_to_list() (in module sage.matrix.matrix_space) dimension() (sage.matrix.matrix_space.MatrixSpace method) dimensions() (sage.matrix.matrix0.Matrix method) dims() (sage.matrix.matrix_space.MatrixSpace method) domain() (sage.matrix.action.MatrixMulAction method) double_det() (in module sage.matrix.matrix_integer_dense_hnf)

E

echelon_form() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense method) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_mpolynomial_dense.Matrix_mpolynomial_dense method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method) (sage.matrix.matrix_rational_sparse.Matrix_rational_sparse method) echelon_in_place() (sage.matrix.matrix_window.MatrixWindow method) echelon_QQ() (in module sage.matrix.benchmark) echelonize() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_mod2_dense.Matrix_mod2_dense method) (sage.matrix.matrix_mod2e_dense.Matrix_mod2e_dense method) (sage.matrix.matrix_modn_dense_double.Matrix_modn_dense_template method) (sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template method) (sage.matrix.matrix_mpolynomial_dense.Matrix_mpolynomial_dense method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method) (sage.matrix.matrix_rational_sparse.Matrix_rational_sparse method) eigenmatrix_left() (sage.matrix.matrix2.Matrix method) eigenmatrix_right() (sage.matrix.matrix2.Matrix method) eigenspaces_left() (sage.matrix.matrix2.Matrix method) eigenspaces_right() (sage.matrix.matrix2.Matrix method) eigenvalues() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) (sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense method) eigenvectors_left() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) (sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense method)

eigenvectors_right() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) (sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense method) element_is_zero() (sage.matrix.matrix_window.MatrixWindow method) elementary_divisors() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_integer_sparse.Matrix_integer_sparse method) elementary_matrix() (in module sage.matrix.constructor) elementwise_product() (sage.matrix.matrix2.Matrix method) exp() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) (sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense method) expand() (sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense method) extended_echelon_form() (sage.matrix.matrix2.Matrix method) extract_ones_data() (in module sage.matrix.matrix_integer_dense_hnf)

F

factor() (sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense method) fcp() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense method) find() (sage.matrix.matrix2.Matrix method) free_m4ri() (in module sage.matrix.matrix_mod2_dense)

frobenius() (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) from_png() (in module sage.matrix.matrix_mod2_dense) full_category_initialisation() (sage.matrix.matrix_space.MatrixSpace method)

G

gcd() (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) gen() (sage.matrix.matrix_space.MatrixSpace method) get_action_impl() (sage.matrix.matrix_space.MatrixSpace method)

get_subdivisions() (sage.matrix.matrix2.Matrix method) get_unsafe() (sage.matrix.matrix_window.MatrixWindow method) gram_schmidt() (sage.matrix.matrix2.Matrix method)

H

H (sage.matrix.matrix2.Matrix attribute) hadamard_bound() (sage.matrix.matrix2.Matrix method) hadamard_row_bound_mpfr() (in module sage.matrix.misc) height() (sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense method) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method) (sage.matrix.matrix_rational_sparse.Matrix_rational_sparse method) hermite_form() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_integer_sparse.Matrix_integer_sparse method) hessenberg_form() (sage.matrix.matrix2.Matrix method)

hessenbergize() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_modn_dense_double.Matrix_modn_dense_template method) (sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template method) hilbert_matrix() (in module sage.matrix.benchmark) hnf() (in module sage.matrix.matrix_integer_dense_hnf) hnf_square() (in module sage.matrix.matrix_integer_dense_hnf) hnf_with_transformation() (in module sage.matrix.matrix_integer_dense_hnf) hnf_with_transformation_tests() (in module sage.matrix.matrix_integer_dense_hnf)

I

I (sage.matrix.matrix2.Matrix attribute) identity_matrix() (in module sage.matrix.constructor) (sage.matrix.matrix_space.MatrixSpace method) image() (sage.matrix.matrix2.Matrix method) indefinite_factorization() (sage.matrix.matrix2.Matrix method) index_in_saturation() (in module sage.matrix.matrix_integer_dense_saturation) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) insert_row() (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) int_range (class in sage.matrix.strassen) integer_kernel() (sage.matrix.matrix2.Matrix method) integer_to_real_double_dense() (in module sage.matrix.change_ring) interleave_matrices() (in module sage.matrix.matrix_integer_dense_hnf) intervals() (sage.matrix.strassen.int_range method) inverse() (sage.matrix.matrix2.Matrix method) inverse_QQ() (in module sage.matrix.benchmark) invert_hilbert_QQ() (in module sage.matrix.benchmark) is_alternating() (sage.matrix.matrix0.Matrix method) is_bistochastic() (sage.matrix.matrix2.Matrix method) is_dense() (sage.matrix.matrix0.Matrix method) (sage.matrix.matrix_space.MatrixSpace method) is_diagonalizable() (sage.matrix.matrix2.Matrix method) is_finite() (sage.matrix.matrix_space.MatrixSpace method) is_hermitian() (sage.matrix.matrix0.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) is_immutable() (sage.matrix.matrix0.Matrix method) is_in_hnf_form() (in module sage.matrix.matrix_integer_dense_hnf)

is_invertible() (sage.matrix.matrix0.Matrix method) is_LLL_reduced() (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) is_Matrix() (in module sage.matrix.matrix) is_MatrixSpace() (in module sage.matrix.matrix_space) is_mutable() (sage.matrix.matrix0.Matrix method) is_normal() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) is_one() (sage.matrix.matrix2.Matrix method) is_permutation_of() (sage.matrix.matrix2.Matrix method) is_positive_definite() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) is_scalar() (sage.matrix.matrix2.Matrix method) is_similar() (sage.matrix.matrix2.Matrix method) is_singular() (sage.matrix.matrix0.Matrix method) is_skew_symmetric() (sage.matrix.matrix0.Matrix method) is_skew_symmetrizable() (sage.matrix.matrix0.Matrix method) is_sparse() (sage.matrix.matrix0.Matrix method) (sage.matrix.matrix_space.MatrixSpace method) is_square() (sage.matrix.matrix0.Matrix method) is_symmetric() (sage.matrix.matrix0.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) is_symmetrizable() (sage.matrix.matrix0.Matrix method) is_unitary() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) is_weak_popov() (sage.matrix.matrix0.Matrix method) iterates() (sage.matrix.matrix0.Matrix method) ith_to_zero_rotation_matrix() (in module sage.matrix.constructor)

J

jordan_block() (in module sage.matrix.constructor)

jordan_form() (sage.matrix.matrix2.Matrix method)

K

kernel() (sage.matrix.matrix2.Matrix method)

kernel_on() (sage.matrix.matrix2.Matrix method)

L

left_eigenmatrix() (sage.matrix.matrix2.Matrix method) left_eigenspaces() (sage.matrix.matrix2.Matrix method) left_eigenvectors() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) left_kernel() (sage.matrix.matrix2.Matrix method) left_nullity() (sage.matrix.matrix2.Matrix method) lift() (sage.matrix.matrix1.Matrix method) (sage.matrix.matrix_modn_dense_double.Matrix_modn_dense_template method) (sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template method) (sage.matrix.matrix_modn_sparse.Matrix_modn_sparse method) linear_combination_of_columns() (sage.matrix.matrix0.Matrix method) linear_combination_of_rows() (sage.matrix.matrix0.Matrix method)

list() (sage.matrix.matrix0.Matrix method) list_to_dict() (in module sage.matrix.matrix_space) LLL() (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method) LLL_gram() (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) log_determinant() (sage.matrix.matrix_double_dense.Matrix_double_dense method) LU() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) LU_valid() (sage.matrix.matrix_double_dense.Matrix_double_dense method)

M

M4RIE_finite_field (class in sage.matrix.matrix_mod2e_dense) Matrix (class in sage.matrix.matrix) (class in sage.matrix.matrix0) (class in sage.matrix.matrix1) (class in sage.matrix.matrix2) matrix() (sage.matrix.matrix_space.MatrixSpace method) (sage.matrix.matrix_window.MatrixWindow method) matrix_add_GF() (in module sage.matrix.benchmark) matrix_add_ZZ() (in module sage.matrix.benchmark) matrix_add_ZZ_2() (in module sage.matrix.benchmark) Matrix_complex_double_dense (class in sage.matrix.matrix_complex_double_dense) Matrix_cyclo_dense (class in sage.matrix.matrix_cyclo_dense) Matrix_dense (class in sage.matrix.matrix_dense) Matrix_double_dense (class in sage.matrix.matrix_double_dense) matrix_from_columns() (sage.matrix.matrix1.Matrix method) (sage.matrix.matrix_modn_sparse.Matrix_modn_sparse method) matrix_from_rows() (sage.matrix.matrix1.Matrix method) (sage.matrix.matrix_modn_sparse.Matrix_modn_sparse method) matrix_from_rows_and_columns() (sage.matrix.matrix1.Matrix method) (sage.matrix.matrix_sparse.Matrix_sparse method) Matrix_generic_dense (class in sage.matrix.matrix_generic_dense) Matrix_generic_sparse (class in sage.matrix.matrix_generic_sparse) Matrix_integer_dense (class in sage.matrix.matrix_integer_dense) matrix_integer_dense_rational_reconstruction() (in module sage.matrix.misc) Matrix_integer_sparse (class in sage.matrix.matrix_integer_sparse) matrix_integer_sparse_rational_reconstruction() (in module sage.matrix.misc) matrix_method() (in module sage.matrix.constructor) Matrix_mod2_dense (class in sage.matrix.matrix_mod2_dense) Matrix_mod2e_dense (class in sage.matrix.matrix_mod2e_dense) Matrix_modn_dense_double (class in sage.matrix.matrix_modn_dense_double) Matrix_modn_dense_float (class in sage.matrix.matrix_modn_dense_float) Matrix_modn_dense_template (class in sage.matrix.matrix_modn_dense_double) (class in sage.matrix.matrix_modn_dense_float) Matrix_modn_sparse (class in sage.matrix.matrix_modn_sparse) Matrix_mpolynomial_dense (class in sage.matrix.matrix_mpolynomial_dense) matrix_multiply_GF() (in module sage.matrix.benchmark) matrix_multiply_QQ() (in module sage.matrix.benchmark)

matrix_multiply_ZZ() (in module sage.matrix.benchmark) matrix_of_variables() (sage.matrix.operation_table.OperationTable method) matrix_over_field() (sage.matrix.matrix1.Matrix method) Matrix_rational_dense (class in sage.matrix.matrix_rational_dense) matrix_rational_echelon_form_multimodular() (in module sage.matrix.misc) Matrix_rational_sparse (class in sage.matrix.matrix_rational_sparse) Matrix_real_double_dense (class in sage.matrix.matrix_real_double_dense) matrix_space() (sage.matrix.matrix1.Matrix method) (sage.matrix.matrix_space.MatrixSpace method) Matrix_sparse (class in sage.matrix.matrix_sparse) Matrix_sparse_from_rows() (in module sage.matrix.matrix_generic_sparse) Matrix_symbolic_dense (class in sage.matrix.matrix_symbolic_dense) matrix_window() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_window.MatrixWindow method) MatrixFactory (class in sage.matrix.constructor) MatrixMatrixAction (class in sage.matrix.action) MatrixMulAction (class in sage.matrix.action) MatrixSpace (class in sage.matrix.matrix_space) MatrixSpace_ZZ_2x2() (in module sage.matrix.matrix_integer_2x2) MatrixVector_QQ() (in module sage.matrix.benchmark) MatrixVectorAction (class in sage.matrix.action) MatrixWindow (class in sage.matrix.matrix_rational_dense) (class in sage.matrix.matrix_window) max_det_prime() (in module sage.matrix.matrix_integer_dense_hnf) maxspin() (sage.matrix.matrix2.Matrix method) minimal_polynomial() (sage.matrix.matrix2.Matrix method) minors() (sage.matrix.matrix2.Matrix method) minpoly() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_modn_dense_double.Matrix_modn_dense_template method) (sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method) (sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense method) mod() (sage.matrix.matrix0.Matrix method) multiplicative_order() (sage.matrix.matrix0.Matrix method) mutate() (sage.matrix.matrix0.Matrix method)

N

n() (sage.matrix.matrix2.Matrix method) N() (sage.matrix.matrix2.Matrix method) ncols() (sage.matrix.matrix0.Matrix method) (sage.matrix.matrix_space.MatrixSpace method) (sage.matrix.matrix_window.MatrixWindow method) ncols_from_dict() (in module sage.matrix.constructor) new_empty_window() (sage.matrix.matrix_window.MatrixWindow method) new_matrix() (sage.matrix.matrix1.Matrix method) new_matrix_window() (sage.matrix.matrix_window.MatrixWindow method) ngens() (sage.matrix.matrix_space.MatrixSpace method) nonpivots() (sage.matrix.matrix0.Matrix method) nonzero_positions() (sage.matrix.matrix0.Matrix method) nonzero_positions_in_column() (sage.matrix.matrix0.Matrix method) nonzero_positions_in_row() (sage.matrix.matrix0.Matrix method)

norm() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) nrows() (sage.matrix.matrix0.Matrix method) (sage.matrix.matrix_space.MatrixSpace method) (sage.matrix.matrix_window.MatrixWindow method) nrows_from_dict() (in module sage.matrix.constructor) nullity() (sage.matrix.matrix2.Matrix method) nullspace_GF() (in module sage.matrix.benchmark) nullspace_RDF() (in module sage.matrix.benchmark) nullspace_RR() (in module sage.matrix.benchmark) nullspace_ZZ() (in module sage.matrix.benchmark) number_of_arguments() (sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense method) numerical_approx() (sage.matrix.matrix2.Matrix method) numpy() (sage.matrix.matrix1.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method)

O

one() (sage.matrix.matrix_space.MatrixSpace method) ones() (in module sage.matrix.matrix_integer_dense_hnf)

ones_matrix() (in module sage.matrix.constructor) OperationTable (class in sage.matrix.operation_table)

P

p (sage.matrix.matrix_modn_sparse.Matrix_modn_sparse attribute) p_saturation() (in module sage.matrix.matrix_integer_dense_saturation) pad_zeros() (in module sage.matrix.matrix_integer_dense_hnf) parity() (in module sage.matrix.matrix_mod2_dense) permanent() (sage.matrix.matrix2.Matrix method) permanental_minor() (sage.matrix.matrix2.Matrix method) permanental_minor_polynomial() (in module sage.matrix.matrix_misc) permutation_normal_form() (sage.matrix.matrix2.Matrix method) permute_columns() (sage.matrix.matrix0.Matrix method) permute_rows() (sage.matrix.matrix0.Matrix method) permute_rows_and_columns() (sage.matrix.matrix0.Matrix method) pfaffian() (sage.matrix.matrix2.Matrix method) pivot_rows() (sage.matrix.matrix2.Matrix method)

pivots() (sage.matrix.matrix0.Matrix method) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_mpolynomial_dense.Matrix_mpolynomial_dense method) pivots_of_hnf_matrix() (in module sage.matrix.matrix_integer_dense_hnf) ple() (in module sage.matrix.matrix_mod2_dense) plot() (sage.matrix.matrix2.Matrix method) pluq() (in module sage.matrix.matrix_mod2_dense) prepare() (in module sage.matrix.constructor) prepare_dict() (in module sage.matrix.constructor) prm_mul() (in module sage.matrix.matrix_misc) probable_hnf() (in module sage.matrix.matrix_integer_dense_hnf) probable_pivot_columns() (in module sage.matrix.matrix_integer_dense_hnf) probable_pivot_rows() (in module sage.matrix.matrix_integer_dense_hnf) prod_of_row_sums() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method)

Q

QR() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method)

R

random_diagonalizable_matrix() (in module sage.matrix.constructor) random_echelonizable_matrix() (in module sage.matrix.constructor) random_element() (sage.matrix.matrix_space.MatrixSpace method) random_matrix() (in module sage.matrix.constructor) random_rref_matrix() (in module sage.matrix.constructor) random_sublist_of_size() (in module sage.matrix.matrix_integer_dense_saturation) random_subspaces_matrix() (in module sage.matrix.constructor) random_unimodular_matrix() (in module sage.matrix.constructor) randomize() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense method) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_mod2_dense.Matrix_mod2_dense method) (sage.matrix.matrix_mod2e_dense.Matrix_mod2e_dense method) (sage.matrix.matrix_modn_dense_double.Matrix_modn_dense_template method) (sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method) rank() (sage.matrix.matrix0.Matrix method) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_mod2_dense.Matrix_mod2_dense method) (sage.matrix.matrix_mod2e_dense.Matrix_mod2e_dense method) (sage.matrix.matrix_modn_dense_double.Matrix_modn_dense_template method) (sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template method) (sage.matrix.matrix_modn_sparse.Matrix_modn_sparse method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method) rank2_GF() (in module sage.matrix.benchmark) rank2_ZZ() (in module sage.matrix.benchmark) rank_GF() (in module sage.matrix.benchmark) rank_ZZ() (in module sage.matrix.benchmark) rational_form() (sage.matrix.matrix2.Matrix method) rational_reconstruction() (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_integer_sparse.Matrix_integer_sparse method) reduced_echelon_matrix_iterator() (in module sage.matrix.echelon_matrix) report() (in module sage.matrix.benchmark) report_GF() (in module sage.matrix.benchmark) report_ZZ() (in module sage.matrix.benchmark) rescale_col() (sage.matrix.matrix0.Matrix method)

rescale_row() (sage.matrix.matrix0.Matrix method) restrict() (sage.matrix.matrix2.Matrix method) restrict_codomain() (sage.matrix.matrix2.Matrix method) restrict_domain() (sage.matrix.matrix2.Matrix method) right_eigenmatrix() (sage.matrix.matrix2.Matrix method) right_eigenspaces() (sage.matrix.matrix2.Matrix method) right_eigenvectors() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) right_kernel() (sage.matrix.matrix2.Matrix method) right_kernel_matrix() (sage.matrix.matrix2.Matrix method) right_nullity() (sage.matrix.matrix2.Matrix method) rook_vector() (sage.matrix.matrix2.Matrix method) round() (sage.matrix.matrix_double_dense.Matrix_double_dense method) row() (sage.matrix.matrix1.Matrix method) (sage.matrix.matrix_mod2_dense.Matrix_mod2_dense method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method) row_iterator() (in module sage.matrix.matrix_misc) row_keys() (sage.matrix.operation_table.OperationTable method) row_module() (sage.matrix.matrix2.Matrix method) row_reduced_form() (in module sage.matrix.matrix_misc) (sage.matrix.matrix2.Matrix method) row_space() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_space.MatrixSpace method) rows() (sage.matrix.matrix1.Matrix method) rref() (sage.matrix.matrix2.Matrix method)

S

sage.matrix.action (module) sage.matrix.benchmark (module) sage.matrix.berlekamp_massey (module) sage.matrix.change_ring (module) sage.matrix.constructor (module) sage.matrix.docs (module) sage.matrix.echelon_matrix (module) sage.matrix.matrix (module) sage.matrix.matrix0 (module) sage.matrix.matrix1 (module) sage.matrix.matrix2 (module) sage.matrix.matrix_complex_double_dense (module) sage.matrix.matrix_cyclo_dense (module) sage.matrix.matrix_dense (module) sage.matrix.matrix_double_dense (module) sage.matrix.matrix_generic_dense (module) sage.matrix.matrix_generic_sparse (module) sage.matrix.matrix_integer_2x2 (module) sage.matrix.matrix_integer_dense (module) sage.matrix.matrix_integer_dense_hnf (module) sage.matrix.matrix_integer_dense_saturation (module) sage.matrix.matrix_integer_sparse (module) sage.matrix.matrix_misc (module) sage.matrix.matrix_mod2_dense (module) sage.matrix.matrix_mod2e_dense (module) sage.matrix.matrix_modn_dense_double (module) sage.matrix.matrix_modn_dense_float (module) sage.matrix.matrix_modn_sparse (module) sage.matrix.matrix_mpolynomial_dense (module) sage.matrix.matrix_rational_dense (module) sage.matrix.matrix_rational_sparse (module) sage.matrix.matrix_real_double_dense (module) sage.matrix.matrix_space (module) sage.matrix.matrix_sparse (module) sage.matrix.matrix_symbolic_dense (module) sage.matrix.matrix_window (module) sage.matrix.misc (module) sage.matrix.operation_table (module) sage.matrix.strassen (module) sage.matrix.symplectic_basis (module) sanity_checks() (in module sage.matrix.matrix_integer_dense_hnf) saturation() (in module sage.matrix.matrix_integer_dense_saturation) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) schur() (sage.matrix.matrix_double_dense.Matrix_double_dense method) set() (sage.matrix.matrix_window.MatrixWindow method) set_block() (sage.matrix.matrix2.Matrix method) set_col_to_multiple_of_col() (sage.matrix.matrix0.Matrix method)

set_column() (sage.matrix.matrix1.Matrix method) set_immutable() (sage.matrix.matrix0.Matrix method) (sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense method) set_max_cols() (in module sage.matrix.matrix0) set_max_rows() (in module sage.matrix.matrix0) set_print_symbols() (sage.matrix.operation_table.OperationTable method) set_row() (sage.matrix.matrix1.Matrix method) set_row_to_multiple_of_row() (sage.matrix.matrix0.Matrix method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method) (sage.matrix.matrix_rational_sparse.Matrix_rational_sparse method) set_to() (sage.matrix.matrix_window.MatrixWindow method) set_to_diff() (sage.matrix.matrix_window.MatrixWindow method) set_to_prod() (sage.matrix.matrix_window.MatrixWindow method) set_to_sum() (sage.matrix.matrix_window.MatrixWindow method) set_to_zero() (sage.matrix.matrix_window.MatrixWindow method) set_unsafe() (sage.matrix.matrix_window.MatrixWindow method) simplify() (sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense method) simplify_rational() (sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense method) simplify_trig() (sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense method) singular_values() (sage.matrix.matrix_double_dense.Matrix_double_dense method) slice() (sage.matrix.matrix_mod2e_dense.Matrix_mod2e_dense method) smith_form() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_integer_sparse.Matrix_integer_sparse method) smithform_ZZ() (in module sage.matrix.benchmark) solve_left() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) solve_right() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) solve_system_with_difficult_last_row() (in module sage.matrix.matrix_integer_dense_hnf) (in module sage.matrix.matrix_integer_dense_saturation) sparse_columns() (sage.matrix.matrix1.Matrix method) sparse_matrix() (sage.matrix.matrix1.Matrix method) sparse_rows() (sage.matrix.matrix1.Matrix method) stack() (sage.matrix.matrix1.Matrix method) (sage.matrix.matrix_mod2e_dense.Matrix_mod2e_dense method) str() (sage.matrix.matrix0.Matrix method) (sage.matrix.matrix_mod2_dense.Matrix_mod2_dense method) strassen_echelon() (in module sage.matrix.strassen) strassen_window_multiply() (in module sage.matrix.strassen) subdivide() (sage.matrix.matrix2.Matrix method) subdivision() (sage.matrix.matrix2.Matrix method) subdivision_entry() (sage.matrix.matrix2.Matrix method) subdivisions() (sage.matrix.matrix2.Matrix method) submatrix() (sage.matrix.matrix1.Matrix method) (sage.matrix.matrix_mod2_dense.Matrix_mod2_dense method) (sage.matrix.matrix_mod2e_dense.Matrix_mod2e_dense method) subs() (sage.matrix.matrix2.Matrix method) subtract() (sage.matrix.matrix_window.MatrixWindow method) subtract_prod() (sage.matrix.matrix_window.MatrixWindow method) SVD() (sage.matrix.matrix_double_dense.Matrix_double_dense method) swap_columns() (sage.matrix.matrix0.Matrix method) swap_rows() (sage.matrix.matrix0.Matrix method) (sage.matrix.matrix_modn_sparse.Matrix_modn_sparse method) (sage.matrix.matrix_window.MatrixWindow method) swapped_columns() (sage.matrix.matrix_mpolynomial_dense.Matrix_mpolynomial_dense method) symplectic_basis_over_field() (in module sage.matrix.symplectic_basis) symplectic_basis_over_ZZ() (in module sage.matrix.symplectic_basis) symplectic_form() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method)

T

T (sage.matrix.matrix2.Matrix attribute) table() (sage.matrix.operation_table.OperationTable method) tensor_product() (sage.matrix.matrix2.Matrix method) test() (in module sage.matrix.strassen) test_trivial_matrices_inverse() (in module sage.matrix.matrix_space) to_list() (sage.matrix.strassen.int_range method)

to_matrix() (sage.matrix.matrix_window.MatrixWindow method) to_png() (in module sage.matrix.matrix_mod2_dense) trace() (sage.matrix.matrix2.Matrix method) trace_of_product() (sage.matrix.matrix2.Matrix method) translation() (sage.matrix.operation_table.OperationTable method) transpose() (sage.matrix.matrix_dense.Matrix_dense method) (sage.matrix.matrix_double_dense.Matrix_double_dense method) (sage.matrix.matrix_integer_dense.Matrix_integer_dense method) (sage.matrix.matrix_mod2_dense.Matrix_mod2_dense method) (sage.matrix.matrix_modn_sparse.Matrix_modn_sparse method) (sage.matrix.matrix_rational_dense.Matrix_rational_dense method) (sage.matrix.matrix_sparse.Matrix_sparse method)

U

unpickle() (in module sage.matrix.matrix0) unpickle_matrix_mod2_dense_v1() (in module sage.matrix.matrix_mod2_dense)

unpickle_matrix_mod2e_dense_v0() (in module sage.matrix.matrix_mod2e_dense)

V

variables() (sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense method) vecmat_ZZ() (in module sage.matrix.benchmark) vector_on_axis_rotation_matrix() (in module sage.matrix.constructor)

VectorMatrixAction (class in sage.matrix.action) visualize_structure() (sage.matrix.matrix2.Matrix method) (sage.matrix.matrix_modn_sparse.Matrix_modn_sparse method)

W

weak_popov_form() (in module sage.matrix.matrix_misc) (sage.matrix.matrix2.Matrix method) wiedemann() (sage.matrix.matrix2.Matrix method) with_added_multiple_of_column() (sage.matrix.matrix0.Matrix method) with_added_multiple_of_row() (sage.matrix.matrix0.Matrix method) with_col_set_to_multiple_of_col() (sage.matrix.matrix0.Matrix method) with_permuted_columns() (sage.matrix.matrix0.Matrix method) with_permuted_rows() (sage.matrix.matrix0.Matrix method)

with_permuted_rows_and_columns() (sage.matrix.matrix0.Matrix method) with_rescaled_col() (sage.matrix.matrix0.Matrix method) with_rescaled_row() (sage.matrix.matrix0.Matrix method) with_row_set_to_multiple_of_row() (sage.matrix.matrix0.Matrix method) with_swapped_columns() (sage.matrix.matrix0.Matrix method) with_swapped_rows() (sage.matrix.matrix0.Matrix method)

Z

zero() (sage.matrix.matrix_space.MatrixSpace method) zero_at() (sage.matrix.matrix_double_dense.Matrix_double_dense method)

zero_matrix() (in module sage.matrix.constructor) (sage.matrix.matrix_space.MatrixSpace method) zigzag_form() (sage.matrix.matrix2.Matrix method)