Elementary Linear Algebra
United States Edition
8th Edition
Published on 18. July 2003
Book
Hardback
656 pages
978-0-13-045787-5 (ISBN)
Description
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.
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.
More details
Edition
8th edition
Language
English
Place of publication
United States
Publishing group
Pearson Education (US)
Target group
Professional and scholarly
Dimensions
Height: 241 mm
Width: 10 mm
Thickness: 10 mm
Weight
1260 gr
ISBN-13
978-0-13-045787-5 (9780130457875)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Bernard Kolman | David Hill
Elementary Linear Algebra with Applications
Book
09/2007
9th Edition
Pearson
€163.40
Article exhausted; check for reprint
Previous edition
Bernard Kolman | David R. Hill
Elementary Linear Algebra
Book
10/1999
7th Edition
Pearson
€49.51
Article exhausted; check for reprint
Content
(NOTE: All relevant chapters end with Supplementary Exercises.)
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.
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.