Introduction to Linear Algebra
4th Edition
Published on 8. December 1997
Book
Hardback
560 pages
978-0-201-82416-2 (ISBN)
Description
This book stresses both practical computation and theoretical principles and centers on the early introduction of matrix theory and systems of linear equations, elementary vector-space concepts, and the eigenvalue problem. Featuring a gradual increase in the level of difficulty, an accessible writing style, and the integration of MATLAB, this text is an excellent introduction for engineering students.
More details
Edition
4th edition
Language
English
Place of publication
United States
Publishing group
Pearson Education (US)
Target group
Professional and scholarly
Dimensions
Width: 244 mm
Thickness: 27 mm
Weight
1030 gr
ISBN-13
978-0-201-82416-2 (9780201824162)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Lee W. Johnson | R. Dean Riess | Jimmy T. Arnold
Introduction to Linear Algebra
United States Edition
Book
11/2001
5th Edition
Pearson
€163.40
Article exhausted; check for reprint
Previous edition
Lee W. Johnson | R.Dean Riess | Jimmy T. Arnold
Introduction to Linear Algebra
Book
12/1992
3rd Edition
Addison Wesley
€32.18
Article exhausted; check for reprint
Content
1. Matrices and Systems of Linear Equations.
Introduction to Matrices and Systems of Linear Equations. Echelon Form and Gauss-Jordan Elimination. Consistent Systems of Linear Equations. Applications. Matrix Operations. Algebraic Properties of Matrix Operations. Linear Independence and Nonsingular Matrices. Data Fitting, Numerical Integration, and Numerical Differentiation. Matrix Inverses and Their Properties.
2. The Vector Space R^n.
Introduction. Vector Space Properties of R^n. Examples of Subspaces. Bases for Subspaces. Dimension. Orthogonal Bases for Subspaces. Linear Transformations from R^n to R^m. Least-Squares Solutions to Inconsistent Systems, with Applications to Data Fitting. Theory and Practice of Least Squares.
3. The Eigenvalue Problem.
Introduction. Determinants and the Eigenvalue Problem. Elementary Operations and Determinants. Eigenvalues and the Characteristic Polynomial. Eigenvectors and Eigenspaces. Complex Eigenvalues and Eigenvectors. Similarity Transformations and Diagonalization. Difference Equations; Markov Chains; Systems of Differential Equations.
4. Vector Spaces and Linear Transformations.
Introduction. Vector Spaces. Subspaces. Linear Independence, Bases, and Coordinates. Dimension. Inner Product Spaces, Orthogonal Bases, and Projections. Linear Transformations. Operations with Linear Transformations. Matrix Representations for Linear Transformations. Change of Basis and Diagonalization.
5. Determinants.
Introduction. Cofactor Expansions of Determinants. Cramer's Rule. Applications of Determinants: Inverses and Wronksians.
6. Eigenvalues and Applications.
Quadratic Forms. Systems of Differential Equations. Transformation to Hessenberg Matrices. Eigenvalues of Hessenberg Matrices. Householder Transformations. The QR Factorization and Least-Squares Solutions. Matrix Polynomials and the Cayley-Hamilton Theorem. Generalized Eigenvectors and Solutions of Systems of Differential Equations.
Appendix A: Introduction to MATLAB.
Appendix B: Review of Geometric Vectors.
Introduction to Matrices and Systems of Linear Equations. Echelon Form and Gauss-Jordan Elimination. Consistent Systems of Linear Equations. Applications. Matrix Operations. Algebraic Properties of Matrix Operations. Linear Independence and Nonsingular Matrices. Data Fitting, Numerical Integration, and Numerical Differentiation. Matrix Inverses and Their Properties.
2. The Vector Space R^n.
Introduction. Vector Space Properties of R^n. Examples of Subspaces. Bases for Subspaces. Dimension. Orthogonal Bases for Subspaces. Linear Transformations from R^n to R^m. Least-Squares Solutions to Inconsistent Systems, with Applications to Data Fitting. Theory and Practice of Least Squares.
3. The Eigenvalue Problem.
Introduction. Determinants and the Eigenvalue Problem. Elementary Operations and Determinants. Eigenvalues and the Characteristic Polynomial. Eigenvectors and Eigenspaces. Complex Eigenvalues and Eigenvectors. Similarity Transformations and Diagonalization. Difference Equations; Markov Chains; Systems of Differential Equations.
4. Vector Spaces and Linear Transformations.
Introduction. Vector Spaces. Subspaces. Linear Independence, Bases, and Coordinates. Dimension. Inner Product Spaces, Orthogonal Bases, and Projections. Linear Transformations. Operations with Linear Transformations. Matrix Representations for Linear Transformations. Change of Basis and Diagonalization.
5. Determinants.
Introduction. Cofactor Expansions of Determinants. Cramer's Rule. Applications of Determinants: Inverses and Wronksians.
6. Eigenvalues and Applications.
Quadratic Forms. Systems of Differential Equations. Transformation to Hessenberg Matrices. Eigenvalues of Hessenberg Matrices. Householder Transformations. The QR Factorization and Least-Squares Solutions. Matrix Polynomials and the Cayley-Hamilton Theorem. Generalized Eigenvectors and Solutions of Systems of Differential Equations.
Appendix A: Introduction to MATLAB.
Appendix B: Review of Geometric Vectors.