有：特征值、特征向量和相似性、酉相似、Schur三角化及其推论、正规矩阵、标准形和包括Jordan标准形在内的各种分解、LU分解、QR分解和酉矩阵、Hermite矩阵和复对称矩阵、向量范数和矩阵范数、特征值的估计和扰动、正定矩阵、非负矩阵。 《矩阵分析.卷1(英文版)(本科)》可作为理工科专业研究生或数学专业高年级本科生教材，也可供数学工作者和科技人员参考。

本书是国际上数值计算方面的权威著作，有“圣经”之称。被美国加州大学、斯坦福大学、华盛顿大学、芝加哥大学、中国科学院研究生院等很多世界知名学府用作相关课程的教材或主要参考书。 本书系统地介绍了矩阵计算的基本理论和方法。书中的许多算法都有现成的软件包实现，每节后还附有习题，并有注释和大量参考文献，非常有助于自学。

From the reviews: "The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity...The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher." --ZENTRALBLATT FUR MATHEMATIK

This book is meant as a short text in linear algebra for a one-term course. Except for an occasional example or exercise the text is logically independent of calculus, and could be taught early. In practice, I expect it to be used mostly for students who have had two or three terms of calculus. The course could also be given simultaneously with, or im mediately after, the first course in calculus. 　　此书为英文版！

线性代数是处理矩阵和向量空间的数学分支科学，在现代数学的各个领域都有应用。《线性代数及其应用(第3版)(英文版)》主要包括线性方程组、矩阵代数、行列式、向量空间、特征值和特征向量、正交性和最小二乘方、对称矩阵和二次型等内容。《线性代数及其应用(第3版)(英文版)》的目的是使学生掌握线性代数最基本的概念、理论和证明。首先以常见的方式，具体介绍了线性独立、子空间、向量空间和线性变换等概念，然后逐渐展开，最后在抽象地讨论概念时，它们就变得容易理解多了。这是一本介绍性的线性代数教材，内容翔实，层次清晰，适合作为高等院校理工科数学课的双语教学用书，也可作为公司职员及工程学研究人员的参考书。

This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.