Commit 2022-03-22 06:15 b0f585c5

View on Github →

feat(combinatorics/simple_graph/inc_matrix): Incidence matrix (#10867) Define the incidence matrix of a simple graph and prove the basics, including some stuff about matrix multiplication.

Estimated changes

Modified src/algebra/ring/basic.lean

added theorem ite_and_mul_zero

Modified src/combinatorics/simple_graph/basic.lean

added theorem simple_graph.card_incidence_finset_eq_degree

deleted theorem simple_graph.incidence_set_inter_incidence_set

added theorem simple_graph.incidence_set_inter_incidence_set_of_adj

added theorem simple_graph.incidence_set_inter_incidence_set_of_not_adj

Created src/combinatorics/simple_graph/inc_matrix.lean

added def simple_graph.inc_matrix

added theorem simple_graph.inc_matrix_apply'

added theorem simple_graph.inc_matrix_apply

added theorem simple_graph.inc_matrix_apply_eq_one_iff

added theorem simple_graph.inc_matrix_apply_eq_zero_iff

added theorem simple_graph.inc_matrix_apply_mul_inc_matrix_apply

added theorem simple_graph.inc_matrix_apply_mul_inc_matrix_apply_of_not_adj

added theorem simple_graph.inc_matrix_mul_transpose

added theorem simple_graph.inc_matrix_mul_transpose_apply_of_adj

added theorem simple_graph.inc_matrix_mul_transpose_diag

added theorem simple_graph.inc_matrix_of_mem_incidence_set

added theorem simple_graph.inc_matrix_of_not_mem_incidence_set

added theorem simple_graph.inc_matrix_transpose_mul_diag

added theorem simple_graph.sum_inc_matrix_apply

added theorem simple_graph.sum_inc_matrix_apply_of_mem_edge_set

added theorem simple_graph.sum_inc_matrix_apply_of_not_mem_edge_set

Modified src/data/finset/card.lean

added theorem finset.card_doubleton

Modified src/data/fintype/basic.lean

added theorem finset.coe_filter_univ

added theorem set.filter_mem_univ_eq_to_finset

Modified src/linear_algebra/affine_space/combination.lean