Description
Clear prose, tight organization, and a wealth of examples and computational techniques make Basic Matrix Algebra with Algorithms and Applications an outstanding introduction to linear algebra. The author designed this treatment specifically for freshman majors in mathematical subjects and upper-level students in natural resources, the social sciences, business, or any discipline that eventually requires an understanding of linear models.
With extreme pedagogical clarity that avoids abstraction wherever possible, the author emphasizes minimal polynomials and their computation using a Krylov algorithm. The presentation is highly visual and relies heavily on work with a graphing calculator to allow readers to focus on concepts and techniques rather than on tedious arithmetic. Supporting materials, including test preparation Maple worksheets, are available for download from the Internet.
This unassuming but insightful and remarkably original treatment is organized into bite-sized, clearly stated objectives. It goes well beyond the LACSG recommendations for a first course while still implementing their philosophy and core material. Classroom tested with great success, it prepares readers well for the more advanced studies their fields ultimately will require.
Table of Contents
SYSTEMS OF LINEAR EQUATIONS AND THEIR SOLUTION
Recognizing Linear Systems and Solutions
Matrices, Equivalence and Row Operations
Echelon Forms and Gaussian Elimination
Free Variables and General Solutions
The Vector Form of the General Solution
Geometric Vectors and Linear Functions
Polynomial Interpolation
MATRIX NUMBER SYSTEMS
Complex Numbers
Matrix Multiplication
Auxiliary Matrices and Matrix Inverses
Symmetric Projectors, Resolving Vectors
Least Squares Approximation
Changing Plane Coordinates
The Fast Fourier Transform and the Euclidean Algorithm.
DIAGONALIZABLE MATRICES
Eigenvectors and Eigenvalues
The Minimal Polynomial Algorithm
Linear Recurrence Relations
Properties of the Minimal Polynomial
The Sequence {Ak}
Discrete dynamical systems
Matrix compression with components
DETERMINANTS
Area and Composition of Linear Functions
Computing Determinants
Fundamental Properties of Determinants
Further Applications
Appendix: The abstract setting
Selected practice problem answers
Index
