arXiv
Open Access
2023
Partial Proof of a Conjecture with Implications for Spectral Majorization
Jeffrey Uhlmann
Abstrak
In this paper we report on new results relating to a conjecture regarding properties of $n\times n$, $n\leq 6$, positive definite matrices. The conjecture has been proven for $n\leq 4$ using computer-assisted sum of squares (SoS) methods for proving polynomial nonnegativity. Based on these proven cases, we report on the recent identification of a new family of matrices with the property that their diagonals majorize their spectrum. We then present new results showing that this family can extended via Kronecker composition to $n>6$ while retaining the special majorization property. We conclude with general considerations on the future of computer-assisted and AI-based proofs.
Penulis (1)
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Jeffrey Uhlmann
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2023
- Bahasa
- en
- Sumber Database
- arXiv
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- Open Access ✓