Elementary Linear Algebra with Applications (9e)

For introductory sophomore-level courses in Linear Algebra or Matrix Theory.

This text presents the basic ideas of linear algebra in a manner that offers students a fine balance between abstraction/theory and computational skills. The emphasis is on not just teaching how to read a proof but also on how to write a proof.

1 - Linear Equations And Matrices

2 - Solving Linear Systems

3 - Determinants

4 - Real Vector Spaces

5 - Inner Product Spaces

6 - Linear Transformations and Matrices

7 - Eigenvalues and Eigenvectors

8 - Applications of Eigenvalues and Eigenvectors (Optional)

9 - MATLAB for Linear Algebra

10 - MATLAB Exercises

A P P E N D I X A Preliminaries

A P P E N D I X B Complex Numbers

A P P E N D I X C Introduction to Proofs

Applications of Eigen value and Eigenvectors (Chapter 8) - new to the edition in this form. It consists of old sections 7.3, 7.5-7.9, 8.1, 8.2

Organizational Changes

• Section 1.7, Computer Graphics, has been expanded
• Old section 2.1 has been split in two sections: 2.1 Echelon Form of a Matrix and 2.2 Solving Linear Systems. This will provided improved pedagogy for covering this important material.
• Old section 3.4 Span and Linear Independence has been split into two sections 3.3 Span and 3.4 Linear Independence.  Since students often have difficulties with these more abstract topics, this revision presents this material at a somewhat slower pace and has more examples.
• Old Chapter 6 Determinants, has now become Chapter 3 to permit earlier coverage of the material.

Exercises involving real world data have been updated to include more recent data sets

• Varied examples of vector spaces have been introduced.
• More exercises at all levels have been added

Discussion has been added to the Chapter Review material. Many of these are suitable for writing projects or group activities.

More applications have been added (including application to networks and chemical balance equations)

More material on recurrence relations

More material discussing the four fundamental subspaces of linear algebra

Strong pedagogical framework.

• Provides students with a strong understanding by gradually introducing topics that connect abstract ideas to concrete foundations.

General level of applications–Presents applications that are suited to a more general audience, rather than for a strongly science-oriented one.

• Enables instructors to use this text for a greater variety of class levels.

Comprehensive supplements–Includes a Student Solutions Manual, an Instructor's Solutions Manual, and a Companion Website.

• Gives both students and instructors valuable course support.

Matrix multiplication in a separate section.

• Gives students more careful coverage of this topic.

Matrix Transformations .

• Introduces geometric applications at a very early stage.

Computer Graphics –Gives an application of matrix transformations.

• Gives students this application earlier, illustrating the concept more fully.

• Extends and generalizes for students the concepts of computer graphics.

Correlation Coefficient –Gives an application of dot product to statistics in a new section.

Search engines–Includes Section 7.9, Dominant Eigenvalue and Principal Component Analysis, and includes several applications of this material.

• Discusses for students the popular search engine Google®, and how it uses the dominant eigenvalue of an enormously large matrix to search the web.

Eigenvalue development includes the complex case.

• Provides a more unified approach.

Appendix on an introduction to proofs.

• Eases students into the abstract aspects of linear algebra.

MATLAB M-files.

• Gives students the more modern versions of these files.

Key terms listed at the end of each section.

Chapter review at the end of each chapter–Includes review True/False questions and Chapter Quiz.

Answers to odd-numbered exercises–Available in a section at the back of the text.

• Enables instructors to use text exercises as graded homework assignments.