Linear Algebra with Applications
Published on 1. April 1998
Book
Hardback
684 pages
978-0-534-95526-7 (ISBN)
Description
This text fully integrates applications and technology into the linear algebra course, and provides coverage of topics such as chaos theory and coding theory. The authors designed this text to be rich in examples, exercises, and applications. It includes all basic linear algebra theory, most important numerical methods and technology.
More details
Language
English
Place of publication
CA
United States
Publishing group
Cengage Learning, Inc
Target group
College/higher education
Illustrations
Illustrations (some col.)
Dimensions
Height: 248 mm
Width: 197 mm
Weight
1202 gr
ISBN-13
978-0-534-95526-7 (9780534955267)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Content
1. Linear systems: Introduction to Linear Systems. Gauss Elimination. Numerical Solutions. 2. Vectors: Vector Operations. Dot Product. Span. Linear Independence. The Product [Ax]. Cross Product. Lines, Planes, and Hyperplanes. 3. Matrices: Matrix Operations. Matrix Inverse. Elementary and Invertible Matrices. LU Factorization. 4. Vector spaces: Subspaces of [R to the n Power]. Vector Spaces. Linear Independence; Bases. Dimension. Coordinate Vectors and Change of Basis. Rank and Nullity. Applications to Coding Theory. 5. Linear transformations: Matrix Transformations. Linear Transformations. Kernel and Range. The Matrix of a Linear Transformation. The Algebra of Linear Transformations. 6. Determinants: Determinants; Cofactor Expansion. Properties of Determinants. The Adjoint; Cramer's Rule. Determinants with Permutations. 7. Eigenvalues and eigenvectors: Eigenvalues and Eigenvectors. Diagonalization. Approximations of Eigenvalues and Eigenvectors. Applications to Dynamical Systems. Applications to Markov Chains. 8. Dot and inner products: Orthogonal Sets and Matrices. Orthogonal Projections; Gram-Schmidt Process. The QR Factorization. Least Squares. Orthogonalization of Symmetric Matrices. Quadratic Forms and Conic Sections. The Singular Value Decomposition (SVD). Inner Products. Appendices: Answers to selected exercises; Each chapter concludes with Applications, Mini-Projects, and Computer Exercises.