Using Maple
Random Matrices
Row And Column Vectors
Dot Products And Matrix Multiplication
Assignments And Procedures
Solving Linear Systems
Matrix Decomposition
Determinants And Norms
Geometry
Special Symbols
Maple Help
Integrated Tutorial

Linear Systems
Linear Equations
Linear Systems
Solving Linear Systems
Matrices And Linear Systems
Augmented Matrices
Row Echelon Matrices
Reduced Row Echelon Matrices
Matrix Equations
Applications
Review

Matrix Algebra
Introduction
Basic Matrix Operations
A Lexicon Of Matrices
Invertible Matrices
Orthogonal Matrices
The Lu Decomposition
Applications
Review

Determinants
The Laplace Expansion
Applications
Review

Vectorspaces
Real Vector Spaces
Bases And Dimension
Subspaces
Complex Vector Spaces
Review

Linear Transformations
Linear Transformations
Matrices Of Linear Transformations
Images And Kernels
Similarity
Review

Eigenvalues And Eigenvectors
Introduction
Characteristic Polynomials
Eigenspaces
Diagonalizing Square Matrices
Applications
Review

Norms And Inner Products
Euclidean Norms And Dot Products
Non-Euclidean Norms
Real Inner Products
Angles
Quadratic Forms
Complex Inner Products
Review

Orthogonality
Orthogonal Vectors
Orthogonal Bases
Orthonormal Bases
The Qr Decomposition
Orthogonal Matrices
Orthogonal Subspaces
Orthogonal Transformations
The Method Of Least Squares
Review

Singular Values And Singular Vectors
Singular Values
Singular Value Decomposition
Applications
Review

A The Fundamental Theorem Of Algebra

B Numerical Calculations

C Mathematical Induction

D Sigmanotation

E Maple Packages
The Combinat Package
The Geometry Package
The Linalg Package
The Linearalgebra Package
The Networks Package
The Plots Package
The Plottools Package
The Stats Package

F Answers To Odd-Numbered Exercises
Linear Systems
Matrix Algebra
Determinants
Vector Spaces
Linear Transformations
Eigenvalues And Eigenvectors
Norms And Inner Products
Orthogonality
Singular Values And Singular Vectors

Index