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by Bernard Kolman and David Hill

Edition: 8TH 04Copyright: 2004

Publisher: Prentice Hall, Inc.

Published: 2004

International: No

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For introductory sophomore-level courses in Linear Algebra or Matrix Theory.

This text presents the basic ideas of linear algebra in a manner that offers students a fine balance between abstraction/theory and computational skills. The emphasis is on not just teaching how to read a proof but also on how to write a proof.

**Features**

- NEW--Improved pedagogy--Divides Chapter 1, Linear Equations and Matrices, into two chapters, laying the foundation for using the idea of matrix function or maps.
- Provides students with an easier format to understand important concepts. Gives instructors the opportunity to present subject matter more comprehensively.

- NEW--Matrix multiplication in a separate section.
- Gives students more careful coverage of this topic.

- NEW--Matrix Transformations--Included in this edition.
- Introduces geometric applications at a very early stage.

- NEW--Computer Graphics--Gives an application of matrix transformations.
- Gives students this application earlier in this edition, illustrating the concept more fully.

- NEW--Improved organization--Moved material in Chapters 1 and 4.
- Provides students with improved exposition and flow of material.

- NEW--Correlation Coefficient--Gives an application of dot product to statistics in a new section.
- NEW--More computer-graphics--Includes Section 5.6, Introduction to Homogeneous Coordinates.
- Extends and generalizes for students the concepts of computer graphics.

- NEW--More on search engines--Includes Section 7.9, Dominant Eigenvalue and Principal Component Analysis, and includes several applications of this material.
- Discusses for students the popular search engine Google®, and how it uses the dominant eigenvalue of an enormously large matrix to search the web.

- NEW--Eigenvalue development includes the complex case.
- Provides a more unified approach.

- NEW--More geometry throughout.
- Offers students a stronger emphasis on the geometrical presentation of basic ideas, and supports this emphasis with an increased use of illustrative ideas.

- NEW--More figures--Increased from 149 figures to 204.
- Gives students more visual aids to increase understanding which is particularly important in the visual world of geometry.

- NEW--Added exercises at all levels--Includes 1603 exercises; exercises are available at the end of each chapter.
- Allows students to more fully explore and study the topics at hand.

- NEW--Upgraded MATLAB M-files.
- Gives students the more modern versions of these files.

- NEW--Key terms listed at the end of each section.
- NEW--Chapter review at the end of each chapter--Includes review True/False questions and Chapter Quiz.
- NEW--Appendix on an introduction to proofs.
- Eases students into the abstract aspects of linear algebra.

- Crisp, conversational tone.
- Enables students to easily follow the style of the text.

- Strong pedagogical framework.
- Provides students with a strong understanding by gradually introducing topics that connect abstract ideas to concrete foundations.

- Answers to odd-numbered exercises--Available in a section at the back of the text.
- Enables instructors to use text exercises as graded homework assignments.

- General level of applications--Presents applications that are suited to a more general audience, rather than for a strongly science-oriented one.
- Enables instructors to use this text for a greater variety of class levels.

- Easy use and readability--Features brief text, smaller trim size, and blue second-color ink.
- Provides students with an easily-read and easily-utilized book.

- Comprehensive supplements--Includes a Student Solutions Manual, an Instructor's Solutions Manual, and a Companion Website.
- Gives both students and instructors valuable course support.

**Kolman, Bernard : Drexel University**

Hill, David R. : Temple University

**1. Linear Equations and Matrices. **

Systems of Linear Equations. Matrices. Matrix Multiplication. Algebraic Properties of Matrix Operations. Special Types of Matrices and Partitioned Matrices. Matrix Transformations. Computer Graphics. Correlation Coefficient (Optional).

**2. Solving Linear Systems. **

Echelon Form of a Matrix. Elementary Matrices: Finding A-1. Equivalent Matrices. LU-Factorization (Optional).

**3. Real Vector Spaces. **

Vectors in the Plane and in 3-space. Vector Spaces. Subspaces. Span and Linear Independence. Basis and Dimension. Homogeneous Systems. Coordinates and Isomorphisms. Rank of a Matrix.

**4. Inner Product Spaces. **

Standard Inner Product on R2 and R3. Cross Product in R3 (Optional). Inner Product Spaces. Gram-Schmidt Process. Orthogonal Complements. Least Squares (Optional).

**5. Linear Transformations and Matrices. **

Definition and Examples. Kernel and Range of a Linear Transformation. Matrix of a Linear Transformation. Vector Space of Matrices and Vector Space of Linear Transformations (Optional). Similarity. Inroduction to Homogeneous Coordinates (Optional).

**6. Determinants. **

Definition. Properties of Determinants. Cofactor Expansion. Inverse of a Matrix. Other Applications of Determinants. Determinants from a Computational Point of View.

**7. Eigenvalues and Eigenvectors. **

Eigenvalues and Eigenvectors. Diagonalization and Similar Matrices. Stable Age Distribution in a Population; Markov Processes (Optional). Diagonalization of Symmetric Matrices. Spectral Decomposition and Singular Value Decomposition (Optional). Real Quadratic Forms. Conic Sections. Quadric Surfaces. Dominant Eigenvalue and Principal Component Analysis (Optional).

**8. Differential Equations (Optional). **

Differential Equations. Dynamical Systems.

**9. MATLAB for Linear Algebra. **

Input and Output in MATLAB. Matrix Operations in MATLAB. Matrix Powers and Some Special Matrices. Elementary Row Operations in MATLAB. Matrix Inverses in MATLAB. Vectors in MATLAB. Applications of Linear Combinations in MATLAB. Linear Transformations in MATLAB. MATLAB Command Summary.

**10. MATLAB Exercises. **Appendix A: Preliminaries.

Sets. Functions.

Appendix B: Complex Numbers.

Complex Numbers. Complex Numbers in Linear Algebra.

Appendix C: Introduction to Proofs.

Answers to Odd-Numbered Exercises.

Index.

Summary

For introductory sophomore-level courses in Linear Algebra or Matrix Theory.

This text presents the basic ideas of linear algebra in a manner that offers students a fine balance between abstraction/theory and computational skills. The emphasis is on not just teaching how to read a proof but also on how to write a proof.

**Features**

- NEW--Improved pedagogy--Divides Chapter 1, Linear Equations and Matrices, into two chapters, laying the foundation for using the idea of matrix function or maps.
- Provides students with an easier format to understand important concepts. Gives instructors the opportunity to present subject matter more comprehensively.

- NEW--Matrix multiplication in a separate section.
- Gives students more careful coverage of this topic.

- NEW--Matrix Transformations--Included in this edition.
- Introduces geometric applications at a very early stage.

- NEW--Computer Graphics--Gives an application of matrix transformations.
- Gives students this application earlier in this edition, illustrating the concept more fully.

- NEW--Improved organization--Moved material in Chapters 1 and 4.
- Provides students with improved exposition and flow of material.

- NEW--Correlation Coefficient--Gives an application of dot product to statistics in a new section.
- NEW--More computer-graphics--Includes Section 5.6, Introduction to Homogeneous Coordinates.
- Extends and generalizes for students the concepts of computer graphics.

- NEW--More on search engines--Includes Section 7.9, Dominant Eigenvalue and Principal Component Analysis, and includes several applications of this material.
- Discusses for students the popular search engine Google®, and how it uses the dominant eigenvalue of an enormously large matrix to search the web.

- NEW--Eigenvalue development includes the complex case.
- Provides a more unified approach.

- NEW--More geometry throughout.
- Offers students a stronger emphasis on the geometrical presentation of basic ideas, and supports this emphasis with an increased use of illustrative ideas.

- NEW--More figures--Increased from 149 figures to 204.
- Gives students more visual aids to increase understanding which is particularly important in the visual world of geometry.

- NEW--Added exercises at all levels--Includes 1603 exercises; exercises are available at the end of each chapter.
- Allows students to more fully explore and study the topics at hand.

- NEW--Upgraded MATLAB M-files.
- Gives students the more modern versions of these files.

- NEW--Key terms listed at the end of each section.
- NEW--Chapter review at the end of each chapter--Includes review True/False questions and Chapter Quiz.
- NEW--Appendix on an introduction to proofs.
- Eases students into the abstract aspects of linear algebra.

- Crisp, conversational tone.
- Enables students to easily follow the style of the text.

- Strong pedagogical framework.
- Provides students with a strong understanding by gradually introducing topics that connect abstract ideas to concrete foundations.

- Answers to odd-numbered exercises--Available in a section at the back of the text.
- Enables instructors to use text exercises as graded homework assignments.

- General level of applications--Presents applications that are suited to a more general audience, rather than for a strongly science-oriented one.
- Enables instructors to use this text for a greater variety of class levels.

- Easy use and readability--Features brief text, smaller trim size, and blue second-color ink.
- Provides students with an easily-read and easily-utilized book.

- Comprehensive supplements--Includes a Student Solutions Manual, an Instructor's Solutions Manual, and a Companion Website.
- Gives both students and instructors valuable course support.

Author Bio

**Kolman, Bernard : Drexel University**

Hill, David R. : Temple University

Table of Contents

**1. Linear Equations and Matrices. **

Systems of Linear Equations. Matrices. Matrix Multiplication. Algebraic Properties of Matrix Operations. Special Types of Matrices and Partitioned Matrices. Matrix Transformations. Computer Graphics. Correlation Coefficient (Optional).

**2. Solving Linear Systems. **

Echelon Form of a Matrix. Elementary Matrices: Finding A-1. Equivalent Matrices. LU-Factorization (Optional).

**3. Real Vector Spaces. **

Vectors in the Plane and in 3-space. Vector Spaces. Subspaces. Span and Linear Independence. Basis and Dimension. Homogeneous Systems. Coordinates and Isomorphisms. Rank of a Matrix.

**4. Inner Product Spaces. **

Standard Inner Product on R2 and R3. Cross Product in R3 (Optional). Inner Product Spaces. Gram-Schmidt Process. Orthogonal Complements. Least Squares (Optional).

**5. Linear Transformations and Matrices. **

Definition and Examples. Kernel and Range of a Linear Transformation. Matrix of a Linear Transformation. Vector Space of Matrices and Vector Space of Linear Transformations (Optional). Similarity. Inroduction to Homogeneous Coordinates (Optional).

**6. Determinants. **

Definition. Properties of Determinants. Cofactor Expansion. Inverse of a Matrix. Other Applications of Determinants. Determinants from a Computational Point of View.

**7. Eigenvalues and Eigenvectors. **

Eigenvalues and Eigenvectors. Diagonalization and Similar Matrices. Stable Age Distribution in a Population; Markov Processes (Optional). Diagonalization of Symmetric Matrices. Spectral Decomposition and Singular Value Decomposition (Optional). Real Quadratic Forms. Conic Sections. Quadric Surfaces. Dominant Eigenvalue and Principal Component Analysis (Optional).

**8. Differential Equations (Optional). **

Differential Equations. Dynamical Systems.

**9. MATLAB for Linear Algebra. **

Input and Output in MATLAB. Matrix Operations in MATLAB. Matrix Powers and Some Special Matrices. Elementary Row Operations in MATLAB. Matrix Inverses in MATLAB. Vectors in MATLAB. Applications of Linear Combinations in MATLAB. Linear Transformations in MATLAB. MATLAB Command Summary.

**10. MATLAB Exercises. **Appendix A: Preliminaries.

Sets. Functions.

Appendix B: Complex Numbers.

Complex Numbers. Complex Numbers in Linear Algebra.

Appendix C: Introduction to Proofs.

Answers to Odd-Numbered Exercises.

Index.

Publisher Info

Publisher: Prentice Hall, Inc.

Published: 2004

International: No

Published: 2004

International: No

For introductory sophomore-level courses in Linear Algebra or Matrix Theory.

This text presents the basic ideas of linear algebra in a manner that offers students a fine balance between abstraction/theory and computational skills. The emphasis is on not just teaching how to read a proof but also on how to write a proof.

**Features**

- NEW--Improved pedagogy--Divides Chapter 1, Linear Equations and Matrices, into two chapters, laying the foundation for using the idea of matrix function or maps.
- Provides students with an easier format to understand important concepts. Gives instructors the opportunity to present subject matter more comprehensively.

- NEW--Matrix multiplication in a separate section.
- Gives students more careful coverage of this topic.

- NEW--Matrix Transformations--Included in this edition.
- Introduces geometric applications at a very early stage.

- NEW--Computer Graphics--Gives an application of matrix transformations.
- Gives students this application earlier in this edition, illustrating the concept more fully.

- NEW--Improved organization--Moved material in Chapters 1 and 4.
- Provides students with improved exposition and flow of material.

- NEW--Correlation Coefficient--Gives an application of dot product to statistics in a new section.
- NEW--More computer-graphics--Includes Section 5.6, Introduction to Homogeneous Coordinates.
- Extends and generalizes for students the concepts of computer graphics.

- NEW--More on search engines--Includes Section 7.9, Dominant Eigenvalue and Principal Component Analysis, and includes several applications of this material.
- Discusses for students the popular search engine Google®, and how it uses the dominant eigenvalue of an enormously large matrix to search the web.

- NEW--Eigenvalue development includes the complex case.
- Provides a more unified approach.

- NEW--More geometry throughout.
- Offers students a stronger emphasis on the geometrical presentation of basic ideas, and supports this emphasis with an increased use of illustrative ideas.

- NEW--More figures--Increased from 149 figures to 204.
- Gives students more visual aids to increase understanding which is particularly important in the visual world of geometry.

- NEW--Added exercises at all levels--Includes 1603 exercises; exercises are available at the end of each chapter.
- Allows students to more fully explore and study the topics at hand.

- NEW--Upgraded MATLAB M-files.
- Gives students the more modern versions of these files.

- NEW--Key terms listed at the end of each section.
- NEW--Chapter review at the end of each chapter--Includes review True/False questions and Chapter Quiz.
- NEW--Appendix on an introduction to proofs.
- Eases students into the abstract aspects of linear algebra.

- Crisp, conversational tone.
- Enables students to easily follow the style of the text.

- Strong pedagogical framework.
- Provides students with a strong understanding by gradually introducing topics that connect abstract ideas to concrete foundations.

- Answers to odd-numbered exercises--Available in a section at the back of the text.
- Enables instructors to use text exercises as graded homework assignments.

- General level of applications--Presents applications that are suited to a more general audience, rather than for a strongly science-oriented one.
- Enables instructors to use this text for a greater variety of class levels.

- Easy use and readability--Features brief text, smaller trim size, and blue second-color ink.
- Provides students with an easily-read and easily-utilized book.

- Comprehensive supplements--Includes a Student Solutions Manual, an Instructor's Solutions Manual, and a Companion Website.
- Gives both students and instructors valuable course support.

**Kolman, Bernard : Drexel University**

Hill, David R. : Temple University

**1. Linear Equations and Matrices. **

Systems of Linear Equations. Matrices. Matrix Multiplication. Algebraic Properties of Matrix Operations. Special Types of Matrices and Partitioned Matrices. Matrix Transformations. Computer Graphics. Correlation Coefficient (Optional).

**2. Solving Linear Systems. **

Echelon Form of a Matrix. Elementary Matrices: Finding A-1. Equivalent Matrices. LU-Factorization (Optional).

**3. Real Vector Spaces. **

Vectors in the Plane and in 3-space. Vector Spaces. Subspaces. Span and Linear Independence. Basis and Dimension. Homogeneous Systems. Coordinates and Isomorphisms. Rank of a Matrix.

**4. Inner Product Spaces. **

Standard Inner Product on R2 and R3. Cross Product in R3 (Optional). Inner Product Spaces. Gram-Schmidt Process. Orthogonal Complements. Least Squares (Optional).

**5. Linear Transformations and Matrices. **

Definition and Examples. Kernel and Range of a Linear Transformation. Matrix of a Linear Transformation. Vector Space of Matrices and Vector Space of Linear Transformations (Optional). Similarity. Inroduction to Homogeneous Coordinates (Optional).

**6. Determinants. **

Definition. Properties of Determinants. Cofactor Expansion. Inverse of a Matrix. Other Applications of Determinants. Determinants from a Computational Point of View.

**7. Eigenvalues and Eigenvectors. **

Eigenvalues and Eigenvectors. Diagonalization and Similar Matrices. Stable Age Distribution in a Population; Markov Processes (Optional). Diagonalization of Symmetric Matrices. Spectral Decomposition and Singular Value Decomposition (Optional). Real Quadratic Forms. Conic Sections. Quadric Surfaces. Dominant Eigenvalue and Principal Component Analysis (Optional).

**8. Differential Equations (Optional). **

Differential Equations. Dynamical Systems.

**9. MATLAB for Linear Algebra. **

Input and Output in MATLAB. Matrix Operations in MATLAB. Matrix Powers and Some Special Matrices. Elementary Row Operations in MATLAB. Matrix Inverses in MATLAB. Vectors in MATLAB. Applications of Linear Combinations in MATLAB. Linear Transformations in MATLAB. MATLAB Command Summary.

**10. MATLAB Exercises. **Appendix A: Preliminaries.

Sets. Functions.

Appendix B: Complex Numbers.

Complex Numbers. Complex Numbers in Linear Algebra.

Appendix C: Introduction to Proofs.

Answers to Odd-Numbered Exercises.

Index.