Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text. Finally, when discussed in the abstract, these concepts are more accessible. It includes easily identifiable Matlab icons in the margins next to Matlab examples and exercises and a CD-Rom bound in the back of the book includes additional Matlab exercises and programs. Instructor's Edition now includes selected solutions and MyMathLab. In this book fundamental ideas of linear algebra are introduced within the first seven lectures, in the concrete setting of Rn, and then gradually examined from different points of view. Later generalizations of these concepts appear as natural extensions of familiar ideas. The focus is on visualization of concepts throughout the book and it has icons in the margins to flag topics for which expanded or enhanced material is available on the Web; a modern view of matrix multiplication is presented. Definitions and proofs focus on the columns of a matrix rather than on the matrix entries; Numerical Notes give a realistic flavor to the text. Students are reminded frequently of issues that arise in the real-life use of linear algebra; and each major concept in the course is given a geometric interpretation because many students learn better when they can visualize an idea.

David C. Lay 在美國加利福尼亞大學獲得碩士和博士學位。他是馬裏蘭大學帕剋學院數學係教授，同時還是阿姆斯特丹大學、阿姆斯特丹自由大學和德國凱澤斯勞滕大學的訪問教授。Lay教授是“綫性代數課程研究小組”的核心成員，發錶瞭30多篇關於泛函分析和綫性代數方麵的論文，並與他人閤著有多部數學教材。