这本书为研究生和本科生课程提供了线性代数的综合知识。作为一个独立的文本，它旨在涵盖该主题的所有重要领域，包括代数结构、矩阵和线性方程组、向量空间、线性变换、对偶和内积空间、正则、双线性、二次、倍线性、厄米特形式的算子和向量空间及其代数的张量积。最后三章的重点是使读者能够在数值方法、解析几何和求解线性微分方程组中寻求线性代数的跨学科应用。每个章节的结尾都有丰富的示例和练习，以增强读者对概念的理解。各种概念的基本知识，如集合、关系、映射等，都是预先假定的。
Advanced Linear Algebra with Applications
This book provides a comprehensive knowledge of linear algebra for graduate and undergraduate courses. As a self-contained text, it aims at covering all important areas of the subject, including algebraic structures, matrices and systems of linear equations, vector spaces, linear transformations, dual and inner product spaces, canonical, bilinear, quadratic, sesquilinear, Hermitian forms of operators and tensor products of vector spaces with their algebras. The last three chapters focus on empowering readers to pursue interdisciplinary applications of linear algebra in numerical methods, analytical geometry and in solving linear system of differential equations. A rich collection of examples and exercises are present at the end of each section to enhance the conceptual understanding of readers. Basic knowledge of various notions, such as sets, relations, mappings, etc., has been pre-assumed.
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