MA 405

COURSE OUTLINE


1. Linear Equations

1.1 Introduction

1.2 Gaussian Elimination And Matrices

1.3 Gauss-Jordan Method

1.5 Making Gaussian Elimination Work

1.6 Ill-Conditioned Systems

2. Rectangular Systems And Echelon Forms

2.1 Row Echelon Form And Rank

2.2 The Reduced Row Echelon Form

2.3 Consistency Of Linear Systems

2.4 Homogeneous Systems

2.5 Nonhomogeneous Systems

3. Matrix Algebra

3.2 Addition, Scalar Multiplication, And Transposition

3.3 Linearity

3.5 Matrix Multiplication

3.6 Properties Of Matrix Multiplication

3.7 Matrix Inversion

3.8 Inverses Of Sums and Sensitivity

3.9 Elementary Matrices And Equivalence

3.10 The LU Factorization

4. Vector Spaces

4.1 Spaces And Subspaces

4.2 Four Fundamental Subspaces

4.3 Linear Independence

4.4 Basis And Dimension

4.5 More About Rank

4.6 Classical Least Squares

5. Norms, Inner Products, and Orthogonality

5.1 Vector Norms And Inner Products

5.2 Orthogonal Vectors

5.3 Gram-Schmidt Procedure

5.4 Unitary and Orthogonal Matrices

6. Determinants

6.1 Determinants

6.2 Additional Properties Of Determinants

7. Eigenvalues And Eigenvectors

7.1 Elementary Properties Of Eigensystems

7.2 Diagonalization by Similarity Transformations

7.3 Functions Of Diagonalizable Matrices