Matrix Analysis and Applications

点击翻译按钮获取中文摘要

Many physical systems (aircraft, string instruments, oceans, skyscrapers, etc.) experience oscillatory behaviour in some form. This behaviour may be beneficial, harmless, or catastrophic depending on the applied loads and the environment. However, mathematical models can be used to analyse vibrations and they have certain mathematical features in common. In particular, in the context of small vibrations linear mathematical/computational models achieve extraordinary success in the prediction and modification of oscillatory systems. Theories have evolved over a period of about three-hundred years, but new mathematical and computational techniques have developed explosively in the last fifty years. Problems in this area provide a major stimulus for my research. However, (as in the past) I also venture into generalizations of these ideas concerning properties of more general matrix and operator-valued functions, and into other areas of application such as mathematical biology, geophysics, and the design of algorithms. In particular, and together with collaborators where appropriate, I plan to continue with research in the direction of so-called "inverse problems", in which performance characteristics are prescribed (generally in the form of spectral data), and then systems are designed to reproduce these characteristics.