I. Syllabus (What we hope to do)

1. Chapter One Matrices and Gaussian Elimination (Much of which is already well known to you)

1.1 Introduction

1.2 The Geometry of Linear Equations

1.3 An Example of Gaussian Elimination

1.4 Matrix Multiplication and Matrix Multiplication

1.5 Triangular Factors and Row Exchanges

1.6 Inverses and Transposes

1.7 **NOT INCLUDED*

2. Chapter Two Vector Spaces

2.1 Vector Spaces and Subspaces

2.2 Solving Ax=b and Ax=0

2.3 Linear Independence, Basis and Dimension

2.4 The four Fundamental Subspaces

2.5 **NOT INCLUDED*

2.6 Linear Transformations

3. Chapter Three Orthogonality

3.1 Orthogonal Vectors and Subspaces

3.2 Cosines and Projections onto Lines

3.3 Projections and Least Squares

3.4 Orthognal Bases and Gram-Schmidt

3.5 The Fast Fourier Transform (* maybe)

4. Chapter Four Determinants

4.1 Introduction

4.2 Properties of the Determinant

4.3 Formulas for he Determinant

4.4 Applications of Determinants

5 Chapter Five Eigenvalues and Eigenvectors

5.1 Introduction

5.2 Diagonalization of a Matrix

5.3 Difference Equations and Powers A^k

5.4 Differential Equations and and e^At

5.5 Complex Matrices

5.6 Sinilarity Transformations

6. Chaptyer Six Positive Definite Matrices

6.1 Minima , Maxima and Saddle Points

6.2 Tests for Positive Definiteness

6.3 The Singular Value Decomposition