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Full 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.
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. SELECTED PRACTICE PROBLEM ANSWERS. INDEX.
