Linear Algebra

This book introduces the recent developments in the subject of quasilinear hyperbolic systems with dissipation, such as frictional damping, relaxation, viscosity and heat diffusion. The mathematical theory behind this subject is emphasized in two ways. One emphasis is based on understanding the influence of the dissipation mechanism on the qualitative behaviour of solutions, such as the nonlinear diffusive phenomena caused by damping, and other phenomena (including phase transition) for the case with viscosity and heat diffusion. The second emphasis is to take the systems with the dissipation mechanism as an approach to approximating the corresponding system of quasilinear hyperbolic conservation laws - the zero-limit relaxation, or the zero-limit viscosity, and the related topic of nonlinear stability of waves Determinants; systems of linear equations; matrix operations; quadratic forms; similar diagonal matrices; Jordan canonical form of matrices; linear spaces and linear transformations; inner product spaces Linear Algebra constitutes a foundation course for those specializing in the fields of mathematics, engineering and science. The course normally takes one semester, but for those needing a more rigorous study of the subject, it involve up to two semesters.This book is based on the lecture notes given for the linear algebra course at the Department of Mathematics in Wuhan University. This work constitutes a foundation course for those specializing in the fields of mathematics, engineering and science. It is based on the lecture notes given for the linear algebra course at the Department of Mathematics in Wuhan University, China. In many practical problems, relations among variables may be simply expressed directly or approximately in terms of linear functions so that it is necessary to investigate such functions.