Finite-Dimensional Linear Algebra (Discrete Mathematics and Its Applications) (Hardcover) by Gockenbach Mark S.
Linear algebra forms the basis for much of modern mathematics-theoretical applied and computational. Finite-Dimensional Linear Algebra provides a solid foundation for the study of advanced mathematics and discusses applications of linear algebra to such diverse areas as combinatorics differential equations optimization and approximation. The author begins with an overview of the essential themes of the book: linear equations best approximation and diagonalization. He then takes students through an axiomatic development of vector spaces linear operators eigenvalues norms and inner products. In addition to discussing the special properties of symmetric matrices he covers the Jordan canonical form an important theoretical tool and the singular value decomposition a powerful tool for computation. The final chapters present introductions to numerical linear algebra and analysis in vector spaces including a brief introduction to functional analysis (infinite-dimensional linear algebra). Drawing on material from the author's own course this textbook gives students a strong theoretical understanding of linear algebra. It offers many illustrations of how linear algebra is used throughout mathematics.