An Algorithm for Diagonalizing Matrices of Formal Power Series
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908822401974272 |
|---|---|
| author | Dai, Zihao Liang, Hao Lu, Jingyu Zhi, Lihong |
| author_facet | Dai, Zihao Liang, Hao Lu, Jingyu Zhi, Lihong |
| contents | This paper studies the unitary diagonalization of matrices over formal power series rings. Our main result shows that a normal matrix is unitarily diagonalizable if and only if its minimal polynomial completely splits over the ring and the associated spectral projections have entries in the ring. Building on this characterization, we develop an algorithm for deciding the unitary diagonalizability of matrices over regular local rings of algebraic varieties. A central ingredient of the algorithm is a decision procedure for determining whether a polynomial splits over a formal power series ring; we establish this using techniques from prime decomposition and the relative smoothness of integral closures in ramification theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08313 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Algorithm for Diagonalizing Matrices of Formal Power Series Dai, Zihao Liang, Hao Lu, Jingyu Zhi, Lihong Commutative Algebra Algebraic Geometry This paper studies the unitary diagonalization of matrices over formal power series rings. Our main result shows that a normal matrix is unitarily diagonalizable if and only if its minimal polynomial completely splits over the ring and the associated spectral projections have entries in the ring. Building on this characterization, we develop an algorithm for deciding the unitary diagonalizability of matrices over regular local rings of algebraic varieties. A central ingredient of the algorithm is a decision procedure for determining whether a polynomial splits over a formal power series ring; we establish this using techniques from prime decomposition and the relative smoothness of integral closures in ramification theory. |
| title | An Algorithm for Diagonalizing Matrices of Formal Power Series |
| topic | Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/2602.08313 |