You are here

Linear Algebra wiith Applications

Gareth Williams
Jones and Bartlett Publishers
Publication Date: 
Number of Pages: 
[Reviewed by
Fernando Q. Gouvêa
, on

See the review of the fifth edition. The main change in this edition is the rearrangement of some of the material. Certain concepts (linear combination, closure, basis, dimension) are introduced earlier in order to prepare students for the more abstract approach introduced in chapter four. The hope is to improve "the uniformity of the level of the material throughout the course." A few new topics and new applications have also been added.


Part 1 Linear Equations, Vectors and Matrices

1.   Linear Equations and Vectors
      1.1   Matrices and Systems of Linear Equations
      1.2   Gauss-Jordan Elimination
      1.3   The Vector Space Rn
      1.4   Basis and Dimension
      1.5   Dot Product, Norm, Angle, and Distance
      1.6   Curve Fitting, Electrical Networks, and Traffic Flow

2.   Matrices and Linear Transformations
      2.1   Addition, Scalar Multiplication, and Multiplication of Matrices
      2.2   Properties of Matrix Operations
      2.3   Symmetric Matrices and Seriation in Archaeology
      2.4   The Inverse of a Matrix and Cryptography
      2.5   Matrix Transformations, Rotations, and Dilations
      2.6   Linear Transformations, Graphics, and Fractals
      2.7   The Leontief Input-Output Model in Economics
      2.8   Markov Chains, Population Movements, and Genetics
      2.9   A Communication Model and Group Relationships in Sociology

3.   Determinants and Eigenvectors
      3.1   Introduction to Determinants
      3.2   Properties of Determinants
      3.3   Determinants, Matrix Inverses, and Systems of Linear Equations
      3.4   Eigenvalues and Eigenvectors
      3.5   Google, Demography, and Weather Prediction

Part 2 Vector Spaces

4.   General Vector Spaces
      4.1   General Vector Spaces
      4.2   Linear Combinations
      4.3   Linear Dependence and Independence
      4.4   Properties of Bases
      4.5   Rank
      4.6   Orthonormal Vectors and Projections
      4.7   Kernal, Range, and the Rank/Nullity Theorem
      4.8   One-to-One Transformations and Inverse Transformations
      4.9   Transformations and Systems of Linear Equations

5.   Coordinate Representations
      5.1   Coordinate Vectors
      5.2   Matrix Representation of Linear Tranformations
      5.3   Diagonalization of Matrices
      5.4   Quadratic Forms, Difference Equations, and Normal Modes

6.   Inner Product Spaces
      6.1   Inner Product Spaces
      6.2   Non-Euclidean Geometry and Special Relativity
      6.3   Approximation of Functions and Coding Theory
      6.4   Least-Squares Curves

Part 3 Numerical Linear Algebra

7.   Numerical Methods
      7.1   Gaussian Elimination
      7.2   The Method of LU Decomposition
      7.3   Practical Difficulties in Solving Systems of Equations
      7.4   Iterative Methods for Solving Systems of Linear Equations
      7.5   Eigenvalues by Iteration; Connectivity of Networks

8.   Linear Programming
      8.1   A Geometrical Introduction to Linear Programming
      8.2   The Simplex Method
      8.3   Geometrical Explanation of the Simplex Method


A.  Cross Product
B.  Equations of Planes and Lines in Three-Space
C.  Graphing Calculator Manual
D.  MATLAB Manual

Answer to Selected Exercises