formal-conjectures · wikipedia · ams-15
Does the determinant of the sum $A + B$ of two $n \times n$ normal
complex matrices $A$ and $B$ always lie in the convex hull
of the $n!$ points $\prod\_i (\lambda(A)\_i + \lambda(B)\_{\sigma(i)})$?
Here the numbers $\lambda(A)\_i$ and $\lambda(B)\_i$ are
the eigenvalues of $A$ and $B$, and $\sigma$ is an element of the symmetric
group $S\_n$.
Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).
Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.
Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://en.wikipedia.org/wiki/Determinantal_conjecture
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Wikipedia/DeterminantalConjecture.lean
Local target: Corpus.WikipediaDeterminantalConjecture.determinantal_conjecture
Source SHA-256: 36715fc041a88c8f1cdfbaf9d311bc02531aa97573d50ecaf4895b7fb848cdbc
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.
Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.
Does the determinant of the sum $A + B$ of two $n \times n$ normal complex matrices $A$ and $B$ always lie in the convex hull of the $n!$ points $\prod\_i (\lambda(A)\_i + \lambda(B)\_{\sigma(i)})$?
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