Status
Available
Call number
Publication
Addison Wesley (2005), Edition: 3, 576 pages
Description
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 so that when discussed in the abstract, these concepts are more accessible.… (more)
User reviews
LibraryThing member IvanIdris
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
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.
Chapter Structure
Each chapter starts with an introductory
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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.
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LibraryThing member danrk
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.
LibraryThing member nmarun
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
I would recommend this book to anyone who is
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interested in learning Linear Algebra. Show Less
Language
Original language
English
Original publication date
1994
Physical description
576 p.; 8.25 inches
ISBN
0321287134 / 9780321287137