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.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Illustrationen
Illustrations (some col.)
Maße
Höhe: 248 mm
Breite: 197 mm
Gewicht
ISBN-13
978-0-534-95526-7 (9780534955267)
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Schweitzer Klassifikation
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.
