David C. Lay (1941–2018)

show more 不错的书，在美国属于知名的教学工作者，搞教学很有一套，虽然算不上厉害的数学家。​

老外的教材，特别是美国的，一般为了清楚地讲明白问题，并加以引申，达到深入浅出的目的，因此页数很多，颇​

此书也不例外，而且另有特点：

1，举了很多应用实例，增加了读者的直观体会，这点往往是国内教材所欠缺的​

2，观点较高，处理方法比较现代，对线性（向量）空间予以足够的关注。说白了，此书的内容不像一些年代久远(​比如文革前)的书，至少当下它不会落伍。​

3，注重了数学软件的应用，当然没有上机条件或不喜编程的人也可以略去不看，不影响的。​

需要注意一点是，习题答案在书后只有约一半，另外一半（偶数号题目）要到网上下载查阅（网址可参考此书前言​

总之，推荐。此书有两个翻译版本，个人推荐华南理工的刘深泉老师版，翻译错误较少。 show less

I had to read “Linear Algebra and Its Applications” by David Lay for the Linear Algebra 1 class in my first semester in University. So this is a gentle introduction to Linear Algebra. The book doesn’t assume a lot of previous knowledge.

Chapter Structure

Each chapter starts with an introductory example. Each section within a chapter ends with practice problems and exercises. Worked out examples with solutions are given too. As you would expect from a Linear Algebra book, there are lots show more of theorems and numerical notes.
1. Systems of Linear Equations

The first chapter gives some examples of linear systems. The row reduction algorithm is explained. I remember having to solve these kind of problems by hand for weeks. As is usual in mathematics, we learn to work out something with paper and pencil the hard way and then we figure out how to do it faster by writing a computer program. If you are into Python, please check out NumPy.
2. Vector and Matrix Equations

Chapter 2 starts with a number of examples as well. We learn about the fundamental idea of representing a linear combination of vectors as a product of a matrix and a vector. This leads to this famous equation:

A x = b
3. Matrix Algebra

Chapter 3 teaches about matrix operations such as matrix multiplication, matrix inversion and transposing matrices. The chapter ends with the Leontief Input Output Model from economics and applications to computer graphics.
4. Determinants

The introductory example in this chapter is about determinants in analytic geometry. Properties of determinants are mentioned as well as calculation methods.
5. Vector Spaces

I don’t know if it has anything to do with the chapter title, but the first example of this chapter is about space flight and control systems. In my opinion this chapter is more theoretical than the preceding chapters. The chapter ends with applications to difference equations and Markov Chains.
6. Eigenvalues and Eigenvectors

Dynamical systems and spotted owls are the topic of the introductory example of chapter 6. This chapter covers amongst others the characteristic equation, diagonalization and iterative algorithms to estimate eigenvalues.
7. Orthogonality and Least Squares

Chapter 7 begins with a short text about the North American Datum. After that we continue with sections on:

orthogonality
orthogonal sets
orthogonal projections
the Gram-Schmidt process
least square problems
inner product spaces

8. Symmetric Matrices and Quadratic Forms

A story about multi channel image processing is the introduction of chapter 8. This chapter has sections on quadratic forms and singular value decomposition.

The book is very readable and entertaining. The diverse list of examples are already reason enough to recommend “Linear Algebra and Its Applications”. I give this book 5 stars out of 5. show less

This is the best linear algebra textbook. Refer to Strang's for better coverage of Vector Spaces and complex matrices, but for everything else, this is the one to use. The study guide is excellent and really complements the textbook well.

Every chapter stats with a practical application of what is being discussed in the rest of the chapter. This helped in building the intuition and useful to solidify those concepts. This is a preliminary book and hence doesn't require much prerequisites.

I would recommend this book to anyone who is interested in learning Linear Algebra.