Elementary Linear Algebra

The hallmark of this text has been the authors' clear, careful, and concise presentation of linear algebra so that students can fully understand how the mathematics works. The text balances theory with examples, applications, and geometric intuition.

• New! Learning Tools CD-ROM will be automatically packaged free with every new text purchased from Houghton Mifflin.
• New! Section 3.4, now named "Introduction to Eigenvalues," has been broken into two separate sections to provide more emphasis on the early introduction of eigenvalues. The new Section 3.5, "Applications of Determinants," covers the Adjoint of a Matrix; Cramer's Rule; and the Area, Volume, and Equations of Lines and Planes.
• New! All real data in exercises and examples have been updated to reflect current statistics and information.
• New! This edition features more Writing Exercises to reinforce critical-thinking skills and additional multi-part True/False Questions in the end-of-section and chapter review exercise sets to encourage students to think about mathematics from different perspectives.
• New! Additional exercises involving larger matrices have been added to the exercise sets where appropriate. These exercises will be linked to the data sets found on the web site and the Learning Tools CD-ROM.
• Guided Proofs help students successfully complete theoretical proofs by leading them, step-by-step, through the logical sequence of statements necessary to reach the correct conclusion.
• Text-specific web site features student and instructor resources, including text Chapters 8 through 10; MATLAB exercises for Chapters 1 through 7; data sets for new matrix problems; and a Graphing Calculator Keystroke Guide featuring the TI-83/TI-83 Plus, TI-86, TI-89, and TI-92 models.

A great book for self-directed learning. Plenty of examples, extraordinary graphics.


best book on the subject i've seen   November 11, 2008
Linda Key (athens, GA)
1 out of 1 found this review helpful

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.


A very good beginning book on Linear Algebra   September 7, 2008
calvinnme (Fredericksburg, Va)
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.


Great textbook!   December 14, 2000
recrandall (Morrisville, NC United States)
2 out of 6 found this review helpful

I'm a Computer Science major at Converse College, and I found this book very user-friendly. (BTW, I have a used copy to sell. Email recrandall@hotmail.com)