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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 and computational (a 3 x 5 matrix describing a store's 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 instructor's taste and to the length of the course. Bronson's 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.
Author Bio
Bronson, Richard : Fairleigh Dickinson University
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.
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 and computational (a 3 x 5 matrix describing a store's 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 instructor's taste and to the length of the course. Bronson's 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.
Author Bio
Bronson, Richard : Fairleigh Dickinson University
Table of Contents
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.