Essential Linear Algebra with Applications

Rooted in a pedagogically successful problem-solving approach to linear algebra, this work fills a gap in the literature that is sharply divided between, on the one end, elementary texts with only limited exercises and examples, and, at the other end, books too advanced in prerequisites and too specialized in focus to appeal to a wide audience. Instead, it clearly develops the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality, while simultaneously emphasizing applications to fields such as biology, economics, computer graphics, electrical engineering, cryptography, and political science.Key features: Intertwined discussion of linear algebra and geometry Example-driven exposition; each section starts with a concise overview of important concepts, followed by a selection of fully-solved problems Over 500 problems are carefully selected for instructive appeal, elegance, and theoretical importance; roughly half include complete solutions Two or more solutions provided to many of the problems; paired solutions range from step-by-step, elementary methods whose purpose is to strengthen basic comprehension to more sophisticated, powerful proofs to challenge advanced readers* Appendices with review material on complex variablesIdeal 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. It can serve as a colorful supplementary problem book, reference, or self-study manual for professional scientists and mathematicians. Complete with bibliography and index, this work is a natural bridge between pure/ applied mathematics and the natural/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.

Numerous applications are treated in fields such as computer science, engineering, and the social sciences Over 500 problems (roughly half solved), often presenting two or more solutions; one more fundamental and elementary, the second more conceptual and sophisticated Can serve as an introductory or advanced undergraduate textbook, a supplementary problem book, a reference work for professionals, and a resource for independent study Includes supplementary material: sn.pub/extras

Autorentext
Titu Andreescu is an Associate Professor of Mathematics at the University of Texas at Dallas.

Klappentext

This textbook provides a rigorous introduction to linear algebra in addition to material suitable for a more advanced course while emphasizing the subject's interactions with other topics in mathematics such as calculus and geometry. A problem-based approach is used to develop the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality.

Key features include:

• a thorough presentation of the main results in linear algebra along with numerous examples to illustrate the theory;

• over 500 problems (half with complete solutions) carefully selected for their elegance and theoretical significance;

• an interleaved discussion of geometry and linear algebra, giving readers a solid understanding of both topics and the relationship between them.

Numerous exercises and well-chosen examples make this text suitable for advanced courses at the junior or senior levels. It can also serve as a source of supplementary problems for a sophomore-level course.

Inhalt

Preface.- Linear Phenomena and Euclidean Spaces of Small Dimension.- Concrete Vector Spaces.- Vector Spaces and Subspaces.- Linear Transformations.- More Matrix Algebra and Determinants.- General Theory of Linear Equations.- Eigenvectors.- Orthogonality.- Forms.- Vector Spaces over Finite Fields.- Appendix A: Complex Numbers.- Appendix B: Polynomials over Complex Numbers.- References.- Index.