Advanced Linear Algebra

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