Chapter 0: Introduction

0-1 About this text

Chapter 1: Vectors and Matrices

1-1 Matrices

1-2 Vectors

1-3 Linear Combinations

1-4 Dot Product (Scalar Product)

1-5 Angles and Orthogonality

1-6 Matrix-Vector Product

1-7 Linear Functions

1-8 Matrix Multiplication

1-9 Matrix Multiplication (continued)

1-10 Graphs

Chapter 2: Systems of Linear Equations and Their Solution Sets

2-1 Systems of Linear Equations

2-2 Elementary Matrices

2-3 Row Reduction And Solution Sets

2-4 Reduced Row Echelon Form (RREF)

2-5 Sets in Rn

2-6 The Set of Solutions

2-7 Bases

2-8 Inverses

2.10 Roundoff Error

Chapter 3: Determinants and Their Applications

3- 1 The Determinant Function

3-2 Volume and the Determinant

3-3 Determinants & Linear Independence

3-4 Cofactor Expansion of a Determinant

3-5 The Adjoint Matrix, Inverses and Cramer's Rule

Chapter 4: Lines and Planes

4-1 Lines in Rn

4-2 Planes in Rn

4-3 The Cross Product

Chapter 5: Applications of the Dot Product

5-1 Projections in Rn

5-2 Projections into a subspace - Orthonormal Basis

5-3 Least Square Solutions to Ax=b

6-1 The Leslie Population Model

6-2 Eigenvalues and Eigenvectors

6-3 Eigenvector Bases

6-4 Dominant Eigenvalues: Principal Component Analysis

6-6 Applications of the Geometric Series: Leontief Models and Markov Chains

6-8 Singular Value Decomposition

6-9 Singular Value Decomposition (continued)

Chapter 7: Linear Transformations

7-1 Linear Transformations

7-2 Change of Basis

7-3 Kernel & Image of a Linear Transformation

8-1 Vector Spaces

8-2 The Vector Space of Infinite Sequences

8-3 Vector Spaces of Functions

8-4 Inner Products in Function Spaces