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Zusatztext Woerdeman’s work requires background knowledge of linear algebra. Students should be familiar with matrix computations, solving systems, eigenvalues, eigenvectors, finding a basis for the null space, row and column spaces, determinants, and inverses. This text provides a more general approach to vector spaces, developing these over complex numbers and finite fields. Woerdeman (mathematics, Drexel Univ.) provides a review of complex numbers and some basic results for finite fields. This book will help build on previous knowledge obtained from an earlier course and introduce students to numerous advanced topics. A few of these topics are Jordan canonical form, the Cayley-Hamilton Theorem, nilpotent matrices, functions of matrices, Hermitian matrices, the tensor product, quotient space, and dual space. The last chapter, which discusses how to use linear algebra, illustrates some applications, such as finding roots of polynomials, algorithms based on matrix vector products, RSA public key inscription, and theoretical topics, such as the Riemann hypothesis and the “P versus NP problem.” Copious exercises are provided, and most give complete solutions. The text will provide a solid foundation for any further work in linear algebra. --R. L. Pour, Emory and Henry College Informationen zum Autor Hugo J. Woerdeman, PhD, professor, Department of Mathematics, Drexel University, Philadelphia, Pennsylvania, USA Klappentext Written in clear and concise language, this book covers the standard topics in a second linear algebra course. The book first introduces general fields and emphasizes matrix algebra over finite fields and complex numbers. It then proceeds to cover vector spaces in depth, addressing vector spaces over general fields. Also discussed are standard topics in linear algebra including linear transformations, Jordan canonical form, inner product spaces, and spectral theory. Additional material covers dual spaces, quotient spaces, and tensor products. It includes well-designed exercises and full solutions to almost all exercises. Zusammenfassung Advanced Linear Algebra features a student-friendly approach to the theory of linear algebra. The author’s emphasis on vector spaces over general fields, with corresponding current applications, sets the book apart. He focuses on finite fields and complex numbers, and discusses matrix algebra over these fields. The text then proceeds to cover vector spaces in depth. Also discussed are standard topics in linear algebra including linear transformations, Jordan canonical form, inner product spaces, spectral theory, and, as supplementary topics, dual spaces, quotient spaces, and tensor products. Written in clear and concise language, the text sticks to the development of linear algebra without excessively addressing applications. A unique chapter on "How to Use Linear Algebra" is offered after the theory is presented. In addition, students are given pointers on how to start a research project. The proofs are clear and complete and the exercises are well designed. In addition, full solutions are included for almost all exercises. Inhaltsverzeichnis Fields and Matrix Algebra. Vector Spaces. Linear Transformations. The Jordan Canonical Form. Inner Product and Normed Vector Spaces. Constructing New Vector Spaces from Given Ones. How to Use Linear Algebra. How to Start Your Own Research Project. Answers to Exercises. ...
