Essential Linear Algebra with Applications: A Problem-Solving Approach

Description

Rooted in a pedagogically successful problem-solving approach to linear algebra, the present work fills a gap in the literature that is sharply divided between elementary texts and books that are too advanced to appeal to a wide audience. It clearly develops the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality, while simultaneously emphasizing applications and connections to fields such as biology, economics, computer graphics, electrical engineering, cryptography, and political science. Ideal as an introduction to linear algebra, the extensive exercises and well-chosen applications also make this text suitable for advanced courses at the junior or senior undergraduate level. Furthermore, it can serve as a colorful supplementary problem book, reference, or self-study manual for professional scientists and mathematicians. Complete with bibliography and index, "Essential Linear Algebra with Applications" is a natural bridge between pure and applied mathematics and the natural and social sciences, appropriate for any student or researcher who needs a strong footing in the theory, problem-solving, and model-building that are the subject’s hallmark. Front Matter....Pages i-x Matrix Algebra....Pages 1-52 Square Matrices of Order 2....Pages 53-83 Matrices and Linear Equations....Pages 85-105 Vector Spaces and Subspaces....Pages 107-148 Linear Transformations....Pages 149-196 Duality....Pages 197-235 Determinants....Pages 237-300 Polynomial Expressions of Linear Transformations and Matrices....Pages 301-338 Diagonalizability....Pages 339-375 Forms....Pages 377-482 Appendix: Algebraic Prerequisites....Pages 483-490 Back Matter....Pages 491-491