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 ag 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. Students' conceptual understanding is reinforced through True/False questions, practice problems, and the use of technology. David Lay changed the face of linear algebra with the execution of this philosophy, and continues his quest to improve the way linear algebra is taught with the new Updated Second Edition.

With this update, he builds on this philosophy through increased visualization in the text, vastly enhanced technology support, and an extensive instructor support package. He has added additional figures to the text to help students visualize abstract concepts at key points in the course. A new dedicated CD and Website further enhance the course materials by providing additional support to help students gain command of difficult concepts. The CD, included in the back of the book, contains a wealth of new materials, with a registration coupon allowing access to a password-protected Website. These new materials are tied directly to the text, providing a comprehensive package for teaching and learning linear algebra. ...Continua

With this update, he builds on this philosophy through increased visualization in the text, vastly enhanced technology support, and an extensive instructor support package. He has added additional figures to the text to help students visualize abstract concepts at key points in the course. A new dedicated CD and Website further enhance the course materials by providing additional support to help students gain command of difficult concepts. The CD, included in the back of the book, contains a wealth of new materials, with a registration coupon allowing access to a password-protected Website. These new materials are tied directly to the text, providing a comprehensive package for teaching and learning linear algebra. ...Continua

Linear Algebra and Its Applications

Ha scritto il 03/02/12

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 Struc

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.

...Continua
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