Three Linear Algebra Questions

9401204汤普森该奖项支持矩阵理论的三个领域的研究。第一个是关于矩阵指数乘积的公式，它的证明引发了一个新的更深层次的问题。首席调查员将致力于解决这个新问题。第二个领域是关于非对易区域上矩阵的矩阵乘积的不变量的研究。第三个研究领域涉及非对易区域上的矩阵的数值范围。开始这些数值极差研究的一个自然位置是具有四元数项的矩阵。本研究属于矩阵理论的一般领域。矩阵是一个矩形阵列。矩阵可以用来表示数学、工程学、统计学、物理学、经济学以及生命和社会科学中的各种情况。

9401204 Thompson This award supports research on three areas in matrix theory. The first concerns a formula for the product of matrix exponentials the proof of which has inspired a new and deeper question. The principal investigator will work on solving this new question. The second area concerns the study of the invariants of matrix products for matrices over a noncommutative domain. The third area of research concerns the numerical range of matrices over a noncommutative domain. A natural place to begin these numerical range studies is with matrices having quaternion entries. This research is in the general area of matrix theory. A matrix is a rectangular array. Matrices can be used to represent a wide variety of situations in mathematics, engineering, statistics, physics, economics, and the life and social sciences.