The numbers of positive definite n×n matrices of given types are summarized in the following table. For example, the three positive eigenvalues 2×2 (0, 1)-matrices are [1 | 0 0 | 1], [1 | 0 1 | 1], [1 | 1 0 | 1], all of which have eigenvalue 1 with degeneracy of two. matrix type | OEIS | counts (0, 1)-matrix | A003024 | 1, 3, 25, 543, 29281, ... (-1, 0, 1)-matrix | A085506 | 1, 5, 133, 18905, ...

acyclic digraph | eigenvalue | positive definite matrix | positive matrix | positive semidefinite matrix | Weisstein's conjecture