Linear Algebra with Applications 7th Edition by Keith Nicholson ISBN 9780070401099 0070401098

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Product details: 

ISBN 10:  0070401098

ISBN 13: 9780070401099

Author: W. Keith Nicholson

This text achieves a balance among computational skills, theories and applications of linear algebra. The contents can be arranged to allow for the presentation of a traditional introduction to linear algebra or a more applied course. More than 330 solved examples are included; many are computational and devoted to applications. This edition leans towards matrix computations and applications, and has a much less abstract focus than the second edition.

Table of contents: 

Chapter 1: Systems of Linear Equations
1.1. Solutions and Elementary Operations
1.2. Gaussian Elimination
1.3. Homogeneous Equations
1.4. An Application to Network Flow
1.5. An Application to Electrical Networks
1.6. An Application to Chemical Reactions

Chapter 2: Matrix Algebra
2.1. Matrix Addition, Scalar Multiplication, and Transposition
2.2. Equations, Matrices, and Transformations
2.3. Matrix Multiplication
2.4. Matrix Inverses
2.5. Elementary Matrices
2.6. Linear Transformations
2.7. LU-Factorization
2.8. An Application to Input-Output Economic Models
2.9. An Application to Markov Chains

Chapter 3: Determinants and Diagonalization
3.1. The Cofactor Expansion
3.2. Determinants and Matrix Inverses
3.3. Diagonalization and Eigenvalues
3.4. An Application to Linear Recurrences
3.5. An Application to Systems of Differential Equations
3.6. Proof of the Cofactor Expansion Theorem

Chapter 4: Vector Geometry
4.1. Vectors and Lines
4.2. Projections and Planes
4.3. More on the Cross Product
4.4. Linear Operations on ℝ³
4.5. An Application to Computer Graphics

Chapter 5: The Vector Space ℝⁿ
5.1. Subspaces and Spanning
5.2. Independence and Dimension
5.3. Orthogonality
5.4. Rank of a Matrix
5.5. Similarity and Diagonalization
5.6. Best Approximation and Least Squares
5.7. An Application to Correlation and Variance

Chapter 6: Vector Spaces (Tổng quát)
6.1. Examples and Basic Properties
6.2. Subspaces and Spanning Sets
6.3. Linear Independence and Dimension
6.4. Finite Dimensional Spaces
6.5. An Application to Polynomials
6.6. An Application to Differential Equations

Chapter 7: Linear Transformations
7.1. Examples and Elementary Properties
7.2. Kernel and Image of a Linear Transformation
7.3. Isomorphisms and Composition
7.4. A Theorem about Differential Equations
7.5. More on Linear Recurrences

Chapter 8: Orthogonality
8.1. Orthogonal Complements and Projections
8.2. Orthogonal Diagonalization
8.3. Positive Definite Matrices
8.4. QR-Factorization
8.5. Computing Eigenvalues
8.6. Complex Matrices
8.7. An Application to Linear Codes over Finite Fields
8.8. An Application to Quadratic Forms
8.9. An Application to Constrained Optimization
8.10. An Application to Statistical Principal Component Analysis (PCA)

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Tags: Keith Nicholson, Linear Algebra