Relation Matrix
A (0, 1)-matrix is an integer matrix in which each element is a 0 or 1. It is also called a logical matrix, binary matrix, relation matrix, or Boolean matrix. The number of m×n binary matrices is 2^(m n), so the number of square n×n binary matrices is 2^(n^2) which, for n = 1, 2, ..., gives 2, 16, 512, 65536, 33554432, ... (OEIS A002416). The numbers of positive eigenvalued n×n (0, 1)-matrices for n = 1, 2, ... are 1, 3, 25, 543, 29281, ... (OEIS A003024). Weisstein's conjecture proposed that these matrices were in one-to-one correspondence with labeled acyclic digraphs on n nodes, and this was subsequently proved by McKay et al. (2003, 2004).
adjacency matrix | Frobenius-König theorem | Gale-Ryser theorem | Hadamard's maximum determinant problem | hard square entropy constant | identity matrix | incidence matrix | integer matrix | Lam's problem | permutation matrix | positive eigenvalued matrix | Redheffer matrix | s-cluster | s-run | Weisstein's conjecture