Matrix Analysis in Engineering and Science

矩阵分析在许多领域都有应用，包括控制理论、微分方程、经济学、电气工程、图论、数值分析、运筹学研究和优化、心理学、量子物理和统计学。然而，这些领域的许多研究人员可能无法利用矩阵分析中的现有结果和证明技术来有效地发展他们的理论，因为他们的专业知识不是矩阵理论，而且他们与矩阵理论研究人员之间缺乏沟通。我们在矩阵分析方面有相当多的经验，并开发、改编或借用了许多技术来研究这一主题。在这个项目中，他们计划开发和应用矩阵方法来解决应用中出现的不同问题。除了证明必要的结果外，我们还将把它们放在更一般和更容易获得的环境中，这样新的结果和技术就可以很容易地被非专业人员使用。矩阵分析是自然科学、社会科学、应用数学、统计学和工程学的基本工具。矩阵是组织和分析数据的一种方式。有时，矩阵分析中的简单结果就是所需要的全部，然而，人们往往需要相当微妙的结果。大多数科学家和工程师只得到了矩阵的介绍。我们将开发和应用矩阵方法来解决各种应用问题，并将我们的结果和技术传播给这些应用领域的研究人员。我们的目标是推进矩阵分析的边界，装备应用研究人员。

MATRIX ANALYSIS IN ENGINEERING AND SCIENCERoy Mathias and Chi-Kwong LiCollege of William and MaryABSTRACTMatrix analysis finds applications in many fields including control theory, differential equations, economics, electrical engineering, graph theory, numerical analysis, operations research and optimization, psychology, quantum physics, and statistics. However, many researchers in these areas may not be able to use the existing results and proof techniques in matrix analysis to develop their theory effectively because their expertise is not in matrix theory and there is a lack of communication between them and researchers in matrix theory. We have considerable experience in matrix analysis and have developed, adapted, or borrowed many techniques to study the subject. In this project, they plan to develop and apply matrixmethods to different problems that arise from applications. In addition to proving the necessary results we will put them in more general and accessible settings, so that the new results andtechniques can be readily used by non-specialists. Matrix analysis is a basic tool in the physical and social sciences, applied mathematics, statistics and engineering. Matrices are a way of organizing and analyzing data. Sometimes simple results in matrix analysis are all that are needed, however, often one needs rather subtle results. Most scientists and engineers receive an only anintroduction to matrices. We will develop and apply matrix methods to a variety of applied problems and will disseminate our results andtechniques to researchers in these applied areas. Our goal is to advance the boundaries in matrix analysis and equip applied researchers.