形式幂级数环上矩阵对角化的算法
An Algorithm for Diagonalizing Matrices of Formal Power Series
AI总结：
本文提出了一种形式幂级数环上矩阵单位ary对角化的算法，基于多项式在环上的分解性质。
摘要：
本文研究了形式幂级数环上矩阵的单位ary对角化问题。我们的主要结果表明，一个正规矩阵单位ary对角化当且仅当其极小多项式在整个环上完全分解，并且相关的谱投影具有环中的元素。基于这一特征，我们开发了一个算法，用于决定代数簇的正则局部环上矩阵的单位ary对角化性。该算法的核心成分是一个决定多项式是否在形式幂级数环上分解的决策过程；我们通过利用素分解技术和分歧理论中的相对光滑性技术来建立这一过程。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
