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
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
More MATLAB exercises have been added.
MATLAB M-files have been upgraded to more modern versions
Discussion has been added to the Chapter Review material. Many of these are suitable for writing projects or group activities.
More geometric material illustrating the discussions of diagonalization of symmetric matrices and singular value decompositions.
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.
General level of applications–Presents applications that are suited to a more general audience, rather than for a strongly science-oriented one.
Comprehensive supplements–Includes a Student Solutions Manual, an Instructor's Solutions Manual, and a Companion Website.
Matrix multiplication in a separate section.
Matrix Transformations .
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.
Eigenvalue development includes the complex case.
Appendix on an introduction to proofs.
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.