Mathematical Sciences: The Invariants of n x n Matrices

数学科学：n x n 矩阵的不变量

• 批准号: 8801967
• 负责人: Edward Formanek
• 金额: $ 7.28万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8801967&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Invariants; Matrices

The project supported concerns the ring of invariants, C(n,r), of a set of r generic nxn matrices over a field K and the trace ring, R(n,r). The main problem is to find presentations for C(n,r) as an algebra over K and R(n,r) as an algebra over C(n,r). The project will also consider the minimal degree of elements in a generating set and whether the quotient field of C(n,r) is purely transcendental over K. The research supported concerns matrix theory, ring theory and the calculation of invariants. In particular, this involves an old problem of determining what mathematical functions are preserved under various transformations. This is of interest in many areas of science as well as in mathematics.

支持的项目涉及域K上的r个泛型nxn矩阵集合的不变量环C（n,r）和迹环r （n,r）。主要的问题是找到C（n,r）在K上的代数表示和r （n,r）在C（n,r）上的代数表示。本项目还将考虑生成集中元素的最小度以及C（n,r）的商域是否纯超越k。支持的研究涉及矩阵理论，环理论和不变量的计算。特别是，这涉及到一个老问题，即确定在各种变换下保留哪些数学函数。这在许多科学领域和数学领域都是令人感兴趣的。