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Linear Algebra With Applications (5TH 13 Edition)

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Linear Algebra With Applications (5TH 13 Edition) Cover

 

Synopses & Reviews

Publisher Comments:

Offering the most geometric presentation available, Linear Algebra with Applications, Fifth Edition emphasizes linear transformations as a unifying theme. This elegant textbook combines a user-friendly presentation with straightforward, lucid language to clarify and organize the techniques and applications of linear algebra. Exercises and examples make up the heart of the text, with abstract exposition kept to a minimum. Exercise sets are broad and varied and reflect the author’s creativity and passion for this course. This revision reflects careful review and appropriate edits throughout, while preserving the order of topics of the previous edition.

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

Product Details

ISBN:
9780321796974
Author:
Bretscher, Otto
Publisher:
Pearson
Subject:
Mathematics-Linear Algebra
Subject:
Advanced
Copyright:
Series:
Featured Titles for Linear Algebra (Introductory)
Publication Date:
20121210
Binding:
Paperback
Language:
English
Pages:
528
Dimensions:
10 x 8.2 x 1 in 1034 gr

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Related Subjects


Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Algebra » Linear Algebra
Science and Mathematics » Mathematics » Basics
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