Mark S. Gockenbach is a professor and chair of the Department of Mathematical Sciences at Michigan Technological University.
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.
Some Problems Posed on Vector Spaces. Fields and Vector Spaces. Linear Operators. Determinants and Eigenvalues. The Jordan Canonical Form. Orthogonality and Best Approximation. The Spectral Theory of Symmetric Matrices. The Singular Value Decomposition. Matrix Factorizations and Numerical Linear Algebra. Analysis in Vector Spaces. Appendices. Bibliography. Index.
This text provides a solid foundation for the study of advanced mathematics and covers many interesting applications of linear algebra, which show how linear algebra is essential in such diverse areas as combinatorics, differential equations, optimization, and approximation. The book discusses important concepts and methods from numerical linear algebra and contains a range of exercises in each section, including some that can be solved using a computer package such as MATLAB®. It also incorporates mini-projects that encourage students to develop topics not covered in the text. A solutions manual is available with qualifying course adoption.
Linear algebra forms the basis for much of modern mathematics - theoretical, applied, and computational. Thsi book provides a foundation for the study of advanced mathematics and discusses applications of linear algebra to such diverse areas as combinatorics, differential equations, optimization, and approximation.
Inhaltsverzeichnis
Some Problems Posed on Vector Spaces. Fields and Vector Spaces. Linear Operators. Determinants and Eigenvalues. The Jordan Canonical Form. Orthogonality and Best Approximation. The Spectral Theory of Symmetric Matrices. The Singular Value Decomposition. Matrix Factorizations and Numerical Linear Algebra. Analysis in Vector Spaces. Appendices. Bibliography. Index.
Klappentext
Linear algebra forms the basis for much of modern mathematics - theoretical, applied, and computational. Thsi book provides a foundation for the study of advanced mathematics and discusses applications of linear algebra to such diverse areas as combinatorics, differential equations, optimization, and approximation.
