Linear Algebra with Applications (Classic Version), 5th edition

  • Otto Bretscher

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Linear Algebra with Applications is your guide to understanding the techniques and applications of linear algebra. Using straightforward language and emphasizing linear transformations as a unifying theme, the text makes complex topics clear and relatable. Instead of relying on abstract exposition, the author offers an abundance of examples and activities to get you hands-on with key concepts. The problems, exercises, and applications provided will help you assess your understanding and master the material.

For the 5th Edition, the text has been thoroughly reviewed and edited, with care to preserve Bretscher's signature, helpful organization. The exercise sets included are broad and varied and reflect the author's creativity and passion for this course.

Published by Pearson (January 1st 2022) - Copyright © 2013

ISBN-13: 9780137848294

Subject: Advanced Math

Category: Linear Algebra

Table of contents

1. Linear Equations

1.1 Introduction to Linear Systems

1.2 Matrices, Vectors, and Gauss-Jordan Elimination

1.3 On the Solutions of Linear Systems; Matrix Algebra


2. Linear Transformations

2.1 Introduction to Linear Transformations and Their Inverses

2.2 Linear Transformations in Geometry

2.3 Matrix Products

2.4 The Inverse of a Linear Transformation


3. Subspaces of Rn and Their Dimensions

3.1 Image and Kernel of a Linear Transformation

3.2 Subspace of Rn; Bases and Linear Independence

3.3 The Dimension of a Subspace of Rn

3.4 Coordinates


4. Linear Spaces

4.1 Introduction to Linear Spaces

4.2 Linear Transformations and Isomorphisms

4.3 The Matrix of a Linear Transformation


5. Orthogonality and Least Squares

5.1 Orthogonal Projections and Orthonormal Bases

5.2 Gram-Schmidt Process and QR Factorization

5.3 Orthogonal Transformations and Orthogonal Matrices

5.4 Least Squares and Data Fitting

5.5 Inner Product Spaces


6. Determinants

6.1 Introduction to Determinants

6.2 Properties of the Determinant

6.3 Geometrical Interpretations of the Determinant; Cramer's Rule


7. Eigenvalues and Eigenvectors

7.1 Diagonalization

7.2 Finding the Eigenvalues of a Matrix

7.3 Finding the Eigenvectors of a Matrix

7.4 More on Dynamical Systems

7.5 Complex Eigenvalues

7.6 Stability


8. Symmetric Matrices and Quadratic Forms

8.1 Symmetric Matrices

8.2 Quadratic Forms

8.3 Singular Values


9. Linear Differential Equations

9.1 An Introduction to Continuous Dynamical Systems

9.2 The Complex Case: Euler's Formula

9.3 Linear Differential Operators and Linear Differential Equations


Appendix A. Vectors

Appendix B: Techniques of Proof

Answers to Odd-numbered Exercises

Subject Index

Name Index

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