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Elementary Linear Algebra, by Ron Larson
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The cornerstone of ELEMENTARY LINEAR ALGEBRA is the authors' clear, careful, and concise presentation of material--written so that readers can fully understand how mathematics works. This program balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system. Featuring a new design that highlights the relevance of the mathematics and improves readability, the Seventh Edition also incorporates new conceptual Capstone exercises that reinforce multiple concepts in each section. Data and applications reflect current statistics and examples to engage users and demonstrate the link between theory and practice.
- Sales Rank: #60560 in Books
- Brand: Brand: Cengage Learning
- Published on: 2012-01-01
- Original language: English
- Number of items: 1
- Dimensions: .80" h x 8.40" w x 10.90" l, 2.55 pounds
- Binding: Hardcover
- 448 pages
- Used Book in Good Condition
Review
1. SYSTEMS OF LINEAR EQUATIONS Introduction to Systems of Equations. Gaussian Elimination and Gauss-Jordan Elimination. Applications of Systems of Linear Equations. 2. MATRICES. Operations with Matrices. Properties of Matrix Operations. The Inverse of a Matrix. Elementary Matrices. Applications of Matrix Operations. 3. DETERMINANTS. The Determinant of a Matrix. Evaluation of a Determinant Using Elementary Operations. Properties of Determinants. Applications of Determinants. 4. VECTOR SPACES. Vectors in Rn. Vector Spaces. Subspaces of Vector Spaces. Spanning Sets and Linear Independence. Basis and Dimension. Rank of a Matrix and Systems of Linear Equations. Coordinates and Change of Basis. Applications of Vector Spaces. 5. INNER PRODUCT SPACES. Length and Dot Product in Rn. Inner Product Spaces. Orthogonal Bases: Gram-Schmidt Process. Mathematical Models and Least Squares Analysis. Applications of Inner Product Spaces. 6. LINEAR TRANSFORMATIONS. Introduction to Linear Transformations. The Kernel and Range of a Linear Transformation. Matrices for Linear Transformations. Transition Matrices and Similarity. Applications of Linear Transformations. 7. EIGENVALUES AND EIGENVECTORS. Eigenvalues and Eigenvectors. Diagonalization. Symmetric Matrices and Orthogonal Diagonalization. Applications of Eigenvalues and Eigenvectors. 8. COMPLEX VECTOR SPACES (online). Complex Numbers. Conjugates and Division of Complex Numbers. Polar Form and Demoivre's Theorem. Complex Vector Spaces and Inner Products. Unitary and Hermitian Spaces. 9. LINEAR PROGRAMMING (online). Systems of Linear Inequalities. Linear Programming Involving Two Variables. The Simplex Method: Maximization. The Simplex Method: Minimization. The Simplex Method: Mixed Constraints. 10. NUMERICAL METHODS (online). Gaussian Elimination with Partial Pivoting. Iterative Methods for Solving Linear Systems. Power Method for Approximating Eigenvalues. Applications of Numerical Methods.
About the Author
Dr. Ron Larson is a professor of mathematics at The Pennsylvania State University, where he has taught since 1970. He received his Ph.D. in mathematics from the University of Colorado and is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson conducts numerous seminars and in-service workshops for math educators around the country about using computer technology as an instructional tool and motivational aid. He is the recipient of the 2013 Text and Academic Authors Association Award for CALCULUS, the 2012 William Holmes McGuffey Longevity Award for CALCULUS: AN APPLIED APPROACH, the 2011 William Holmes McGuffey Longevity Award for PRECALCULUS: REAL MATHEMATICS, REAL PEOPLE, and the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS (a complete text on CD-ROM that was the first mainstream college textbook to be offered on the Internet). Dr. Larson authors numerous textbooks including the best-selling Calculus series published by Cengage Learning.
Most helpful customer reviews
27 of 28 people found the following review helpful.
A very good beginning book on Linear Algebra
By calvinnme
I really like the layout and presentation of subject matter in this textbook. If you want to self-teach, I can't think of a better companion text. Everything is clearly laid out in detail. It is oriented towards college sophomore and juniors who are also students of engineering or computer science. Knowledge of calculus is not required, although there are a couple of examples that use calculus that are clearly labeled and can be omitted without loss of continuity. There are theorems and proofs included, but this is very much an applied example-driven book. There is an abundance of diagrams and figures illustrating every point and example. There is currently a sixth edition, but if you can convince your instructor, go for this edition. I've seen the sixth edition and it offers no better a presentation than this one. Has matrix algebra somehow changed in the last five years? I don't think so. The following is the table of contents:
1. Systems of Linear Equations
2. Matrices
3. Determinants
4. Vector Spaces
5. Inner Product Spaces
6. Linear Transformations
7. Eigenvalues and Eigenvectors
8. Complex Vector Spaces
The book has something extra special - every chapter has a section that shows how the material just presented figures into the solution of an actual problem. The following is the list of applications for each chapter:
1. Applications of Systems of Linear Equations
a. Polynomial Curve Fitting
b. Network Analysis
2. Applications of Matrix Operations
a. Stochastic Matrices
b. Crypotography
c. Leontief Input-Output Models
d. Least Squares Regression Analysis
3. Applications of Determinants
a. The adjoint of a matrix
b. Cramer's Rule
c. Area, Volume, and Equations of lines and planes
4. Applications of Vector spaces
a. Linear Differential Equations
b. Conic sections and rotation
5. Applications of inner product spaces
a. The cross product of two vectors in space
b. Least squares approximations
c. Fourier approximations
6. Applications of Linear Transformations
a. Geometry of linear transformations in the plane.
b. Computer graphics
7. Applications of eigenvectors and eigenvalues
a. Population growth
b. Systems of differential equations
c. Quadratic equations
Each of the first seven chapters also has two projects each which range from the very simple to the involved.
14 of 14 people found the following review helpful.
best book on the subject i've seen
By Linda Key
i was a math major at University of Georgia (i have graduated since then) and took intro to linear algebra several times. (okay it's not THAT funny.) it was a different teacher and a different book every time. which made it very easy for me to compare. this book was so much more organized and explained things so much better so that not only did i pass the class, i actually made an A. strongly recommended for all that is interested in the subject, or taking this class but having difficulties. this book will help you understand.
9 of 10 people found the following review helpful.
Linear Algebra
By Eric G.
This book isn't the worst but it is certainly not the best. I took this course at my university and the book wasn't used that much. We would use this book in recitation after lecture. The excercises range from easy to hard rather quickly. The worst chapter in this book had to be that of Chapter 4 Section 7 : Coordinates and Change of Basis. This chapter was by far the most challenging and I hated it with a passion just because I am not the best student when it comes to identifying conics. I thank my teacher for his brilliant lectures, it made this book easier to navigate. But this book isn't that bad, for me the highlight of this book is that it pushes the student out of their comfort zone with strenuous problems that go from shifting the x and y axis according to theta to showing that a statement is true by writing a proof.
I do not recommend this book however for those who would like to self study. If any linear algebra book is worth buying for self study, I would recommend Linear Algebra by Gilbert Strang, just because his lectures (which revolve around his book) are posted for free on youtube.
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