Linear Algebra

An Introduction
Erscheinungsjahr 1995
ISBN: 978-0-12-135245-5
Verlag: Elsevier Science & Technology

Buch, Englisch, 504 Seiten, Format (B × H): 191 mm x 235 mm

In this appealing and well-written text, Richard Bronson gives readers a substructure for a firm understanding of the abstract concepts of linear algebra and its applications. The author starts with the concrete andcomputational (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). The first three chapters address the basics: matrices, vector spaces, and linear transformations. The next three cover eigenvalues, Euclidean inner products, and Jordan canonical forms, offering possibilities that can be tailored to the instructors taste and to the length of the course. Bronsons approach to computation is modern and algorithmic, and his theory is clean and straightforward. Throughout, the views of the theory presented are broad and balanced. Key material is highlighted in the text and summarized at end of each chapter. The book also includes ample exercises with answers and hints. With its inclusion of all the needed pedagogical features, this text will be a pleasure for teachers and students alike.

- 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.

Bronson, Richard

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie

Inhaltsverzeichnis

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.