Inertia semantics

Inertia is the triple (n_pos, n_neg, n_zero) — the number of positive, negative, and zero eigenvalues of a symmetric matrix. feral reports an inertia alongside every factorization.

Guarantees

• Non-singular matrices: inertia is exact.
• Singular matrices: on matrices where the canonical Fortran direct solvers (MUMPS 5.8.2 and SPRAL SSIDS) disagree on inertia, feral agrees with at least one of them.

The corpus consensus framework lives under external_benchmarks/consensus/ and tags matrices with no 3-of-4-oracle agreement as excluded; those matrices are not part of the inertia gate.

See Inertia in the API reference for the type itself.