Matrix Theory and Its Applications

Author: Huang Youdu, Zhu Shixin / Country: Mainland China
Publisher:
Publish Date: 2005-08-01
Features: Matrix theory is based on linear algebra, requiring learners to have a solid grasp of the fundamental concepts and computational methods of linear algebra and be able to apply them proficiently. This book is divided into six chapters. Chapter 1 is Linear Spaces and Linear Transformations, serving as a connection point with linear algebra. The content of this chapter has been briefly introduced in linear algebra, and here it is reviewed, supplemented, and enhanced. Chapter 2 covers Inner Product Spaces, introducing the concept of inner product in linear spaces. Chapter 3 discusses the concepts and computations of matrix eigenvalues and Jordan canonical forms. Chapter 4 deals with Matrix Norms and Power Series, introducing norms for vectors and matrices, and explaining matrix power series and methods for determining their convergence. Chapter 5 is Matrix Functions and Their Applications, serving as an interface between the abstract theories of the preceding chapters and practical applications. Chapter 6 covers the Estimation of Matrix Eigenvalues and Generalized Inverse Matrices, introducing methods for estimating matrix eigenvalues and introducing the concept of generalized inverse matrices.