Linear Algebra and Its Applications

by David C. Lay

NOTE: This edition features the same content as the traditional text in a convenient, three-hole-punched, loose-leaf version. Books a la Carte also offer a great value--this format costs significantly less than a new textbook. Before purchasing, check with your instructor or review your course syllabus to ensure that you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, including customized versions for individual schools, and registrations are not transferable. In addition, you may need a CourseID, provided by your instructor, to register for and use Pearson's MyLab & Mastering products.
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For courses in linear algebra. With traditional linear algebra texts, the course is relatively easy for students during the early stages as material is presented in a familiar, concrete setting. However, when abstract concepts are introduced, students often hit a 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. These concepts are fundamental to the study of linear algebra, so students' understanding of them is vital to mastering the subject. This text makes these concepts more accessible by introducing them early in a familiar, concrete Rn setting, developing them gradually, and returning to them throughout the text so that when they are discussed in the abstract, students are readily able to understand. Also available with MyMathLab MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. MyMathLab includes assignable algorithmic exercises, the complete eBook, interactive figures, tools to personalize learning, and more.

Genres: Mathematics, Textbooks, Reference, Nonfiction, Science, School, Academic

592 pages, Paperback

First published December 1, 1993

Reviews

[Micah · Rating 4 out of 5]

a bit thin on plot

[trivialchemy · Rating 3 out of 5]

When he was a schoolchild, the story goes, future German mathematician Carl Friedrich Gauss was ordered by his arithmetic teacher to sum all the numbers between 1 and 100 -- a ruse to keep his pupils busy. In a flash of providential insight, young Gauss realized that the pairwise sums of numbers from both ends of the set (1+100, 2+99, 3+98) were each 101. The solution, which he produced immediately, was simply 50 times this: 5050.

[Ivan Idris · Rating 5 out of 5]

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 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.

[Kenta Suzuki · Rating 5 out of 5]

Although I have not read cover to cover, this book contains good pictures(positive definite, negative definite, etc.)which are good for visual learner. For visual leaner, I definitely recommend awesome videos about linear algebra by 3Blue1Brown , https://www.youtube.com/watch?v=kjBOe... .

[Hai Le · Rating 5 out of 5]

An excellent book with very clear explanations and many concrete examples. The content of the book focuses more on the conceptual than the computational side of linear algebra. So in my opinion, it would make a great start for those who begin to learn linear algebra or want to refresh their understanding after a long time not using it.

[Alyosha · Rating 4 out of 5]

As an undergrad student who has never learned math voluntarily before, I think this book is great for beginners. It provides an intuitive image of what is actually happening. More often than not, it does a good job at translating the formula to a sensible sentence, and throughout reading this book it made me realize that mathematical formula isn't more than a language.

[Kristen · Rating 4 out of 5]

Linear Algebra is not what it seems at first thought. Fascinating way of looking and solving for space in all dimensions. I enjoyed this book

[Emelie Granbom · Rating 1 out of 5]

Insett jag kan lägga till kurslitteratur 😎 swag

[Joe Tran · Rating 4 out of 5]

PRETTY good book. I do recommend for taking MA 265 at Purdue. Concepts made much more simple but certainly not my favorite branch of math. Much too abstract for my engineering brain.

[Jaslyn]

gr8 as intro material.

[Allison Hartley]

the book had me living in the matrix all semester 😵‍💫

[Phong Ly]

dope.

[Matt · Rating 4 out of 5]

A good, if basic, textbook for linear algebra. I wish that the two online chapters had been printed in the book, especially the chapter covering Markov chain processes.

[evelyn · Rating 5 out of 5]

going from this amazing textbook to discrete may have been the biggest loss of my life

[Nathan Albright · Rating 4 out of 5]

I'm not going to lie; this was a very boring book.  In all fairness, the book is a college level textbook in linear algebra, and few people would read such a book for their personal amusement as I did, so I will not judge it too harshly or not being particularly exciting, because I had no expectations that it would be so.  That said, this book does have ambitions of being relevant, if not exciting, and it is certainly intriguing and worthwhile to see how it is that the book encourages readers to pay attention to the relevance of its subjects, even if that subject is not the most exciting or interesting thing in the world.  Although this textbook seems to be the sort of book that the Manga Guide to Linear Algebra was written in response to, but all the same it is worthwhile to note that this book does try--very hard--to demonstrate the practical importance of linear algebra even if its approach is not very interesting and even if its style is particularly leaden.  It reminded me that knowledge of a subject's relevance and a desire to convey the importance of subject matter is not sufficient to make something exciting to read.

This book is about 500 pages long and is divided into seven chapters.  The first chapter discusses linear equations in linear algebra, introducing the book's concepts (1), which takes up the first 100 pages or so.  After that the author discusses matrix algebra, with plenty of problems to help the student master the material (2).  A short chapter on determinants follows, which includes Cramer's rule (3), before the author moves on to discuss vector spaces and questions of rank and various applications (4) of the subject.  This leads into a chapter on eigenvalues and eigenvectors that shows applications to differential equations and spotted owls (5).  The author then concludes the main section of the book with a chapter on orthogonality and the least squares method (6) that provides plenty of applications and then a closing chapter on symmetric matrices and quadratic forms that deals with constraint optimization and other applications (7).  After this there are appendices on the uniqueness of the reduced echelon form (A) as well as complex numbers (B) for those who want additional material on these subjects, before the book concludes with a glossary, answers to odd-numbered exercises, and an index of the book's materials.

In reading a book like this, even if I have no particular driving need to familiarize myself with linear algebra, I was reminded of the sort of appeal which teachers and textbook writers often use when it comes to mathematics subjects, and that is the push towards pointing out the applications of subjects.  To be sure, there are many applications of linear algebra and it is a very useful subject, as are many aspects of math and science and related subjects.  It was striking, though, to wonder why it was that the author of this book did not seek to inspire a certain degree of passion or creativity when it comes to the subject.  It is one thing to know that there are many ways to use a subject and many jobs where a given subject comes in handy, but it is an entirely different thing to be filled with a degree of passion and enthusiasm to solve particular problems in the world today through mastery of a technical field like linear algebra.  Contrary to this book's overwhelming dullness (and reading it was I was falling asleep was certainly a very bad idea), this subject is worth more than just attempts to cure insomnia.

[Ho Sing · Rating 4 out of 5]

I used this for a graduate course for non-mathematics major.

In a mathematics textbook, I value graphicality the most, meaning each concepts and theorems are not only laid out in a manner that is easy to grasp, but allow readers to develop a concept model in their brains that can aid long term memory. I believe this textbook did quite well in this aspect, and I could understand most of theorems without much difficulty.

However, what this textbook suffers from is a tendency to oversimplify the explanations and examples, especially in the more advanced topics like Principle Component Analysis. While it certainly encourages readers to link the logical steps on their own, I felt like this challenge compromises my understanding of some of the concepts.

That said, this is a great textbook for non-mathematics major that finds mathematical writing style too exotic.

[Tiffany · Rating 4 out of 5]

linear algebra & matrices

[Jerzy · Rating 5 out of 5]

Clear and well-organized, with many helpful explanations and illustrations.

[Rob Bennett · Rating 2 out of 5]

Paying for a textbook and flipping to the back to see an answer or brief explanation only to see "check the study guide" which costs additional money is pretty irritating.

[Aaron Rossi · Rating 4 out of 5]

This is an excellent textbook for anyone trying to learn Linear Algebra.

It offers an excellent introduction to the subject and covers all the essential topics of Undergraduate Linear Algebra. It also covers some special topics such as the Principal Axes Theorem, Constrained Optimization, Singular Value Decomposition, and Geometry. Each chapter also discusses applications and fun computation facts about the topic, such as computational pitfalls and workarounds. It also contains some references to excellent books and papers for special topics if the student wishes to learn more.

The only downside of the book is it can be a bit hand-wavy at times and, hence, may not be rigorous enough for some people. There are also some things, such as the Jordan Canonical form, which I wish the book covered. However, these are usually reserved for a more advanced treatment.

Nevertheless, this is an excellent book if you are looking at learning Linear Algebra. It's a very nice introduction to the topic.

Nevertheless, this is an excellent

[Dominic Foo · Rating 4 out of 5]

A good introduction to undergraduate linear algebra, good balance of theoretical proofs and applications. The best feature of this book, in my opinion, is their reference to previous theorems and results when it comes to more advanced theorems. I think though that a lot of its attempt to show the use of linear algebra for other topics or in practical application engages in a bit too much handwaving to enable us truly grasp what was going on.

But overall a good introduction to the topic.

[Elise Hedlund · Rating 4 out of 5]

On today's installment of "Rating my college textbooks because if I have to read them, they better count toward my Goodreads challenge!" we have my lin alg textbook. While seeing this book again is rather traumatizing, it did in fact help me greatly during the class. The examples in the textbook made doing the homework a much easier process, and while I'm still confused on the point of linear algebra and much of how it works, this book did help me get a solid introduction, so I'll take it!!

[Arun Mahendrakar · Rating 4 out of 5]

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.

[Helena · Rating 4 out of 5]

The book is a comprehensive introduction to linear algebra and incorporates some examples of practical applications. I would recommend supplementing learnings from this book with materials that could allow for a better conceptual understanding of the constructs of the linear algebraic system, such as 3Blue1Brown's Essence of Linear Algebra YouTube video series.

[Snorlax · Rating 5 out of 5]

This is probably more easy to understand than Gilbert Strang's book https://www.goodreads.com/book/show/1...

I respect both professors a lot. However, a good textbook should be self-evident, unlike Gilbert Strang's which requires you to go through MIT videos.

[Viktor · Rating 4 out of 5]

This is a good introductory textbook. It's readable, has lots of examples and a handful of problems, which cover both theory and practice. There are full solutions available online, which is great for the self-learner. Although some chapters could be improved, Mr. Lay has done a very good job with "Linear Algebra and Its Applications".

[Lecture Freed · Rating 1 out of 5]

I dislike the way David C. Lay approaches the subject of linear algebra. The excessive formalism and overall lack of personality makes it hard for me as a reader to relate to the subject.

[Guozhang Chen · Rating 5 out of 5]

Great book. Very clear, I only read the eigenvale and eigenvector chapter, it is better than that in Gilbert's book.

[Hamed Mahdavi · Rating 4 out of 5]

Good book to start linear algebra, but not enough for advanced usage.

[Klock Robbie · Rating 4 out of 5]

not sure if gilbert strang would’ve done it better. shame we didn’t get into dimension earlier in the book. wish it painted the bigger picture sooner instead of waiting until eigenvalues