An Introduction
Buch, Englisch, 504 Seiten, Format (B × H): 191 mm x 235 mm
ISBN: 978-0-12-135245-5
Verlag: Elsevier Science & Technology
- Gives a firm substructure for understanding linear algebra and its applications
- Introduces deductive reasoning and helps the reader develop a facility with mathematical proofs
- Begins with the concrete and computational (a 3 x 5 matrix describing a stores inventory) and leads the reader to a choice of major applications (Markov chains, least squares approximation, and solution of differential equations using Jordan normal form)
- Covers matrices, vector spaces, linear transformations, as well as applications to Jordan canonical forms, differential equations, and Markov chains
- Gives computational algorithms for finding eigenvalues and eigenvectors
- Provides a balanced approach to computation and theory
- Highlights key material in the text as well as in summaries at the end of each chapter
- Includes ample exercises with answers and hints, in addition to other learning features
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Matrices: Basic Concepts. Matrix Multiplication. Special Matrices. Linear Systems of Equations. The Inverse. LU Decomposition. Properties of R
n. Vector Spaces: Vectors. Subspaces. Linear Independence. Basis and Dimension. Row Space of a Matrix. Rank of a Matrix. Linear Transformations: Functions. Linear Transformations. Matrix Representations. Change of Basis. Properties of Linear Transformations. Eigenvalues and Eigenvectors: Determinants. Properties of Determinants. Eigenvectors and Eigenvalues. Properties of Eigenvalues and Eigenvectors. Diagonalization. Power Methods. Markov Chains. Euclidean Inner Products: Orthogonality. Projections. The QR-Algorithm. Least Squares. Orthogonal Complements. Jordan Canonical Forms: Invariant Subspaces. Jordan Canonical Forms. The Exponential Function. Differential Equations in Fundamental Form. Solving Differential Equations in Fundamental Form. Chapter Reviews. Answers and Hints to Selected Problems. Subject Index.