矩阵理论引论

Chapter 1 Introduction to Linear Algebra 1.1 The linear space 1.1.1 Fields and mappings 1.1.2 Definition of the linear space 1.1.3 Basis and dimension 1.1.4 Coordinate 1.1.5 Transformations of bases and coordinates 1.1.6 Subspace and the dimension theorem for vector spaces 1.2 Linear transformation and matrices 1.2.1 Linear transformation 1.2.2 Matrices of linear transformations and isomorphism 1.3 Eigenvalues and the Jordan canonical form 1.3.1 Eigenvalues and eigenvectors 1.3.2 Diagonal matrices 1.3.3 Schur's theorem and the Cayley- Hamilton theorem 1.3.4 The Jordan canonical form 1.4 Unitary spaces Exercise 1Chapter 2 Matrix Analysis 2.1 Vector norm 2.2 Matrix norm 2.3 Matrix sequences and series 2.4 Matrix function 2.5 Differentiation and integration of matrices 2.6 Applications of matrix functions 2.7 Estimation of eigenvalues Exercise 2Chapter 3 Matrix Decomposition 3.1 QR decomposition 3.2 Full rank decomposition 3.3 Singular value decomposition 3.4 The spectral decomposition Exercise 3Chapter 4 Generalized Inverse 4.1 The generalized inverse of a matrix 4.2 A{1},A{1,3} andA{1,4} 4.3 The Moore- Penrose inverse A 4.4 The generalized inverses and the linear equations Exercise 4Chapter 5 Tensor Product 5.1 Definition and properties of the tensor product 5.2 The tensor product and eigenvalues 5.3 Straighten operation on matrices 5.4 The tensor product and matrix equation Exercise 5Chapter 6 Introduction To Nonnegative Matrices 6.1 Preliminary properties on nonnegative matrices 6.2 Positive matrices and the Perron theorem 6.3 Irreducible nonnegative matrices 6.4 Primitive matrices and M matrices 6.5 Stochastic matrices 6.6 Two models of nonnegative matrices Exercise 6References

《矩阵理论引论》由李红裔、赵迪编著。　　《矩阵理论引论》讲述了： This textbook contains six chapters, covering reviews on linear algebra; matrix functions;matrix decompositions such as singular value decompositions and spectral decompositions; generalized inverses;tensor product and nonnegative matrices. Each chapter includes many examples and problems to help students master the presented material.There are no prerequisites except for some basic knowledge on linear algebra. This book aims to provide the material for a basic matrix theory course to senior undergraduates or postgraduates in science and engineering, and can be used as a self- contained reference for a variety of readers.

李红裔、赵迪编著的《矩阵理论引论》偏重于矩阵理论中的计算部分，重点阐述基本概念、具有重要应用背景的定理公式，并提供了大量的算例来帮助读者理解。本书共分六章，涵盖了一般矩阵论课程所讲述的内容。具体包括矩阵范数、矩阵函数、矩阵分解（如QR分解、谱分解、满秩分解、奇异值分解）、广义矩阵逆、张量积、非负矩阵等。本书可作为工科高年级本科生或低年级研究生的矩阵论课程的教学用书。此外，本书也可作为相关领域科研工作者、工程开发人员等的参考资料。