Mathematical Sciences: Problems in Linear Algebra

数学科学：线性代数问题

• 批准号: 8901059
• 负责人: Robert Thompson
• 金额: --
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1993-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901059&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Linear; Algebra

A variety of problems in finite dimensional linear algebra are to be investigated. These include the properties of the exponent, the invariant factors of a product of integral matrices, the eigenvalues of a sum of Hermitian matrices, the matrix valued norm inequality comparing a matrix valued norm of a product to the matrix norm of its factors, and a conjecture that geometry underlies many spectral inequalities for matrices. This project is concerned with research in matrix theory. A matrix is a rectangular array whose entries can come from a wide variety of rings including the integers, the complex numbers and the real numbers. Matrices are valuable in many branches of mathematics, as well as, physics, chemistry and engineering.

有限维线性代数中的各种问题有待研究。其中包括指数的性质，积分矩阵的乘积的不变因子，Hermitian矩阵的特征值之和，矩阵值范数不等式比较乘积的矩阵值范数与其因子的矩阵范数，以及一个猜想，即矩阵的许多谱不等式的几何基础。这个项目是关于矩阵理论的研究。矩阵是一个矩形数组，它的元素可以来自各种各样的环，包括整数、复数和真实的数。矩阵在数学、物理、化学和工程学的许多分支中都有重要的价值。