Description
Book SynopsisThis book provides a comprehensive knowledge of linear algebra for graduate and undergraduate courses. As a self-contained text, it aims at covering all important areas of the subject, including algebraic structures, matrices and systems of linear equations, vector spaces, linear transformations, dual and inner product spaces, canonical, bilinear, quadratic, sesquilinear, Hermitian forms of operators and tensor products of vector spaces with their algebras. The last three chapters focus on empowering readers to pursue interdisciplinary applications of linear algebra in numerical methods, analytical geometry and in solving linear system of differential equations. A rich collection of examples and exercises are present at the end of each section to enhance the conceptual understanding of readers. Basic knowledge of various notions, such as sets, relations, mappings, etc., has been pre-assumed.
Table of Contents1. Algebraic Structures
2. Matrices and Systems of Linear Equations
3. Vector Spaces
4. Linear Transformations
5. Dual Spaces
6. Inner Product Spaces
7. Canonical Forms of an Operator
8. Bilinear and Quadratic Forms
9. Sesquilinear and Hermitian Forms
10. Applications of Linear Algebra to Numerical Methods
11. Affine and Euclidean Spaces and the Applications of Linear Algebra to Geometry
12. Ordinary differential equations and linear systems of ordinary differential equations
