Linear Algebra, James R. Kirkwood and Bessie H. Kirkwood, 978-1-4987-7685-1, K29751
Shelving Guide: Mathematics
This text has a major focus on demonstrating facts and techniques of linear systems that will be invaluable in higher mathematics and related fields. A linear algebra course has two major audiences that it must satisfy. It provides an important theoretical and computational tool for nearly every discipline that uses mathematics. It also provides an introduction to abstract mathematics.
This book has two parts. Chapters 1–7 are written as an introduction. Two primary goals of these chapters are to enable students to become adept at computations and to develop an understanding of the theory of basic topics including linear transformations. Important applications are presented.
Part two, which consists of Chapters 8–14, is at a higher level. It includes topics not usually taught in a first course, such as a detailed justification of the Jordan canonical form, properties of the determinant derived from axioms, the Perron–Frobenius theorem and bilinear and quadratic forms.
Though users will want to make use of technology for many of the computations, topics are explained in the text in a way that will enable students to do these computations by hand if that is desired.
Key features include:
- Chapters 1–7 may be used for a first course relying on applications
- Chapters 8–14 offer a more advanced, theoretical course
- Definitions are highlighted throughout
- MATLAB® and R Project tutorials in the appendices
- Exercises span a range from simple computations to fairly direct abstract exercises
- Historical notes motivate the presentation
Chapter 1. Matrices. Chapter 2. Systems of Linear Equations. Chapter 3. Vector Spaces. Chapter 4. Linear Transformations. Chapter 5. Eigenvalues and Eigenvectors. Chapter 6. Inner Product Spaces. Chapter 7. Linear Functional, Dual Spaces, and Adjoint Operators. Chapter 8. Two Decompositions of a Matrix. Chapter 9. Determinants. Chapter 10. The Jordan Canonical Form. Chapter 11. Applications of the Jordan Canonical Form. Chapter 12. The Perron–Frobenius Theorem. Chapter 13. Bilinear Forms. Chapter 14. Introduction to Tensor Product. Appendix I. A brief guide to MATLAB. Appendix II. An introduction to R. Answers to selected exercises.
Biography
Jim Kirkwood holds a Ph.D. from University of Virginia. He has had ten mathematics textbooks published on various topics including calculus, real analysis, mathematical biology and mathematical physics. His newest text is "Markov Processes," published by Taylor and Francis, and will be out in January, 2015. His original research was in mathematical physics, and he co-authored the seminal paper in a topic now called Kirkwood-Thomas Theory in mathematical physics. During the summer, he teaches real analysis to entering graduate students at the University of Virginia. He has been awarded several National Science Foundation grants.
