Linear Algebra with Applications 2nd Edition Bretscher Solutions Manual

Linear Algebra with Applications 2nd Edition Bretscher Solutions Manual

Product details:

• ISBN-10 ‏ : ‎ 0130198579
• ISBN-13 ‏ : ‎ 978-0130198570
• Author: Otto Bretscher

With the most geometric presentation now available, this reference emphasizes linear transformations as a unifying theme, and enables users to “do” both computational and abstract math in each chapter. A second theme is introduced half way through the text—when eigenvectors are reached—on dynamical systems. It also includes a wider range of problem sets than found in any other book in this market. Chapter topics include systems of linear equations; linear transformations; subspaces of Rn and their dimension; linear spaces; orthogonality and least squares; determinants; eigenvalues and eigenvectors; symmetric matrices and quadratic forms; and linear differential equations. For anyone seeking an introduction to linear algebra.

Table 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

Appendix A. Vectors

Appendix B: Techniques of Proof

Answers to Odd-numbered Exercises

Subject Index

Name Index

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